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.
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
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.
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.
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.
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.
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.
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.
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.
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
Mathematical Modelling with Differential Equations
This book aims to introduce various strategies for modeling systems using differential equations. Some of these methodologies are elementary and quite direct to comprehend and apply while others are complex in nature and require thoughtful, deep contemplation.
Cambridge Lower Secondary Complete Mathematics 8 Student Book 2nd Edition Set
Numerical Analysis and Computational Mathematics
Mathematical modeling is an active area of applied mathematics. At its beginning, engineers were the main practitioners of this area of mathematics, developing mathematical models to solve engineering problems in natural sciences. However, analysis methods and models in social sciences are similar to those of nature sciences, including engineering, with the only difference being that instead of using principles of the nature, one uses principles or theories from experts of such social sciences. Models based on ordinary or partial differential equations describe a wide variety of phenomena such as sound, heat, diffusion, electrostatics, electrodynamics, fluid dynamics, elasticity, or quantum mechanics, for example. Further, stochastic models have recently received increasing attention. Obviously, some of these types of complex problems also require a deep analysis of the tools utilized to solve these situations. In this collection, we will attempt to integrate models, methods, and also applications, not only in the scope of traditional natural sciences, but also opening the scope to education and other social sciences. Theory and data-driven models, even in a synergy that gives rise to producing fertile, multidisciplinary, and hybrid models, can be considered.
Robust Microelectronic Devices
Integrated electronic circuits have influenced our society over the past decades and have become an indispensable part of our daily lives. To maintain this development and ensure benefits for decades to come, continuous further development of electronic chips is necessary. These developments include improving their performance and universality and exploiting the full potential of microelectronic technologies. An important issue for all microelectronic devices is their robustness, i.e., the high performant and reliable function, which is the key for long-term failure safe and stable operation of complex electrical circuits and applications. In real devices, the high-performant and stable operation becomes limited by various physical effects, such as bias temperature instabilities, stress-induced leakage currents, etc. A continuous improvement of the physical understanding of such effects is essential for further optimization of silicon transistors and the improvement of the performance of emerging technologies such as devices based on wide bandgap materials like SiC or GaN as well as for novel 2D transistors. The publications published in this special issue cover various aspects of robust electronic devices and are just as diverse as the field of research itself.
Fractal Analysis: Basic Concepts and Applications
The aim of this book is to provide a basic and self-contained introduction to the ideas underpinning fractal analysis. The book illustrates some important applications issued from real data sets, real physical and natural phenomena as well as real applications in different fields, and consequently, presents to the readers the opportunity to implement fractal analysis in their specialties according to the step-by-step guide found in the book.Besides advanced undergraduate students, graduate students and senior researchers, this book may also serve scientists and research workers from industrial settings, where fractals and multifractals are required for modeling real-world phenomena and data, such as finance, medicine, engineering, transport, images, signals, among others.For the theorists, rigorous mathematical developments are established with necessary prerequisites that make the book self-containing. For the practitioner often interested in model building and analysis, we provide the cornerstone ideas.
Chemotaxis Modeling of Autoimmune Inflammation
This book is directed to the computer-based modeling of chemotaxis inflammation, typically resulting from an infection by a pathogen (e.g., bacteria, viruses). The book has particular relevance to the coronavirus pandemic since long-Covid neurological impairment may be the result of brain inflammation.
Information Retrieval and Natural Language Processing
This book gives a comprehensive view of graph theory in informational retrieval (IR) and natural language processing(NLP). This book provides number of graph techniques for IR and NLP applications with examples. It also provides understanding of graph theory basics, graph algorithms and networks using graph. The book is divided into three parts and contains nine chapters. The first part gives graph theory basics and graph networks, and the second part provides basics of IR with graph-based information retrieval. The third part covers IR and NLP recent and emerging applications with case studies using graph theory. This book is unique in its way as it provides a strong foundation to a beginner in applying mathematical structure graph for IR and NLP applications. All technical details that include tools and technologies used for graph algorithms and implementation in Information Retrieval and Natural Language Processing with its future scope are explained in a clear and organized format.
Smart Materials and Devices for Energy Harvesting
This book is devoted to energy harvesting from smart materials and devices. It focusses on the latest available techniques recently published by researchers all over the world.Energy Harvesting allows otherwise wasted environmental energy to be converted into electric energy, such as vibrations, wind and solar energy.It is a common experience that the limiting factor for wearable electronics, such as smartphones or wearable bands, or for wireless sensors in harsh environments, is the finite energy stored in onboard batteries. Therefore, the answer to the battery "charge or change" issue is energy harvesting because it converts the energy in the precise location where it is needed. In order to achieve this, suitable smart materials are needed, such as piezoelectrics or magnetostrictives. Moreover, energy harvesting may also be exploited for other crucial applications, such as for the powering of implantable medical/sensing devices for humans and animals.Therefore, energy harvesting from smart materials will become increasingly important in the future. This book provides a broad perspective on this topic for researchers and readers with both physics and engineering backgrounds.
Geometrical Theory of Analytic Functions
The book contains papers published in the Mathematics Special Issue, entitled "Geometrical Theory of Analytic Functions". Fifteen papers devoted to the study concerning complex-valued functions of one variable present new outcomes related to special classes of univalent functions, differential equations in view of geometric function theory, quantum calculus and its applications in geometric function theory, operators and special functions associated with differential subordination and superordination theories and starlikeness, and convexity criteria.
Spatial Networks
This book provides a complete introduction into spatial networks. It offers the mathematical tools needed to characterize these structures and how they evolve in time and presents the most important models of spatial networks.The book puts a special emphasis on analyzing complex systems which are organized under the form of networks where nodes and edges are embedded in space. In these networks, space is relevant, and topology alone does not contain all the information. Characterizing and understanding the structure and the evolution of spatial networks is thus crucial for many different fields, ranging from urbanism to epidemiology.This subject is therefore at the crossroad of many fields and is of potential interest to a broad audience comprising physicists, mathematicians, engineers, geographers or urbanists. In this book, the author has expanded his previous book ("Morphogenesis of Spatial Networks") to serve as a textbook and reference on this topic for a wide range of students and professional researchers.
Inverse Optimal Control and Inverse Noncooperative Dynamic Game Theory
This book presents a novel unified treatment of inverse problems in optimal control and noncooperative dynamic game theory. It provides readers with fundamental tools for the development of practical algorithms to solve inverse problems in control, robotics, biology, and economics. The treatment involves the application of Pontryagin's minimum principle to a variety of inverse problems and proposes algorithms founded on the elegance of dynamic optimization theory. There is a balanced emphasis between fundamental theoretical questions and practical matters. The text begins by providing an introduction and background to its topics. It then discusses discrete-time and continuous-time inverse optimal control. The focus moves on to differential and dynamic games and the book is completed by consideration of relevant applications. The algorithms and theoretical results developed in Inverse Optimal Control and Inverse Noncooperative Dynamic Game Theory provide new insights into information requirements for solving inverse problems, including the structure, quantity, and types of state and control data. These insights have significant practical consequences in the design of technologies seeking to exploit inverse techniques such as collaborative robots, driver-assistance technologies, and autonomous systems. The book will therefore be of interest to researchers, engineers, and postgraduate students in several disciplines within the area of control and robotics.
Computational Optimizations for Machine Learning
The present book contains the 10 articles finally accepted for publication in the Special Issue "Computational Optimizations for Machine Learning" of the MDPI journal Mathematics, which cover a wide range of topics connected to the theory and applications of machine learning, neural networks and artificial intelligence. These topics include, among others, various types of machine learning classes, such as supervised, unsupervised and reinforcement learning, deep neural networks, convolutional neural networks, GANs, decision trees, linear regression, SVM, K-means clustering, Q-learning, temporal difference, deep adversarial networks and more.It is hoped that the book will be interesting and useful to those developing mathematical algorithms and applications in the domain of artificial intelligence and machine learning as well as for those having the appropriate mathematical background and willing to become familiar with recent advances of machine learning computational optimization mathematics, which has nowadays permeated into almost all sectors of human life and activity.
Fuzzy Sets in Business Management, Finance, and Economics
This book collects fifteen papers published in s Special Issue of Mathematics titled "Fuzzy Sets in Business Management, Finance, and Economics", which was published in 2021. These paper cover a wide range of different tools from Fuzzy Set Theory and applications in many areas of Business Management and other connected fields. Specifically, this book contains applications of such instruments as, among others, Fuzzy Set Qualitative Comparative Analysis, Neuro-Fuzzy Methods, the Forgotten Effects Algorithm, Expertons Theory, Fuzzy Markov Chains, Fuzzy Arithmetic, Decision Making with OWA Operators and Pythagorean Aggregation Operators, Fuzzy Pattern Recognition, and Intuitionistic Fuzzy Sets. The papers in this book tackle a wide variety of problems in areas such as strategic management, sustainable decisions by firms and public organisms, tourism management, accounting and auditing, macroeconomic modelling, the evaluation of public organizations and universities, and actuarial modelling.We hope that this book will be useful not only for business managers, public decision-makers, and researchers in the specific fields of business management, finance, and economics but also in the broader areas of soft mathematics in social sciences. Practitioners will find methods and ideas that could be fruitful in current management issues. Scholars will find novel developments that may inspire further applications in the social sciences.
Resolvability In Soft Topological Spaces
In this book, we used the concept of soft sets and we studied the soft sets theory as an analytical study and dividing the kinds to four families, to make a comparison between them and identify similarities and differences among them, then we chooses one of these families to be the focus of our work is the fourth family, all of this in order to we get the concepts of the resolvability and irresolvability in soft topological spaces .
Einstein's Violin
Music brings great joy to many of us. But its other benefits often go underappreciated. Numerous studies and historical anecdotes highlight how powerfully music alters the human mind. Two characteristics drive most of music's cognitive benefits: It builds a faster highway between the right and left sides of the brain, enabling greater cooperation between the logical and the creative. It also creates a vast mesh of connectivity within the brain, like a microcosm of the World Wide Web. In a fascinating study, Douglas Wadle celebrates the juxtaposition of art and science while examining music's influence on humanity's understanding of our place in the universe. Tracing the millennia-old love affair between music and science, Wadle chronicles the surprising ubiquity of musical training among history's greatest thinkers. He shines a spotlight on the intertwining stories of pattern and form and how they complement one another in our search for creativity and insight. Einstein's Violin relies on extensive research to tell the story of how music impacts the pattern recognition software in our brains, facilitating more creative problem solving. Without digression into technical treatise, it focuses on the historical stories that best display music's beautiful interaction with mind and universe.
Einstein's Violin
Music brings great joy to many of us. But its other benefits often go underappreciated. Numerous studies and historical anecdotes highlight how powerfully music alters the human mind. Two characteristics drive most of music's cognitive benefits: It builds a faster highway between the right and left sides of the brain, enabling greater cooperation between the logical and the creative. It also creates a vast mesh of connectivity within the brain, like a microcosm of the World Wide Web. In a fascinating study, Douglas Wadle celebrates the juxtaposition of art and science while examining music's influence on humanity's understanding of our place in the universe. Tracing the millennia-old love affair between music and science, Wadle chronicles the surprising ubiquity of musical training among history's greatest thinkers. He shines a spotlight on the intertwining stories of pattern and form and how they complement one another in our search for creativity and insight. Einstein's Violin relies on extensive research to tell the story of how music impacts the pattern recognition software in our brains, facilitating more creative problem solving. Without digression into technical treatise, it focuses on the historical stories that best display music's beautiful interaction with mind and universe.
Theoretical Computer Science for the Working Category Theorist
Using basic category theory, this Element describes all the central concepts and proves the main theorems of theoretical computer science. Category theory, which works with functions, processes, and structures, is uniquely qualified to present the fundamental results of theoretical computer science. In this Element, readers will meet some of the deepest ideas and theorems of modern computers and mathematics, such as Turing machines, unsolvable problems, the P=NP question, Kurt G繹del's incompleteness theorem, intractable problems, cryptographic protocols, Alan Turing's Halting problem, and much more. The concepts come alive with many examples and exercises.
Theoretical Computer Science and Discrete Mathematics
This book includes 15 articles published in the Special Issue "Theoretical Computer Science and Discrete Mathematics" of Symmetry (ISSN 2073-8994). This Special Issue is devoted to original and significant contributions to theoretical computer science and discrete mathematics. The aim was to bring together research papers linking different areas of discrete mathematics and theoretical computer science, as well as applications of discrete mathematics to other areas of science and technology. The Special Issue covers topics in discrete mathematics including (but not limited to) graph theory, cryptography, numerical semigroups, discrete optimization, algorithms, and complexity.
Recent Advances and Future Trends in Nanophotonics
Nanophotonics has emerged as a multidisciplinary frontier of science and engineering. Due to its high potential to contribute to breakthroughs in many areas of technology, nanophotonics is capturing the interest of many researchers from different fields.This Special Issue of Applied Sciences on "Recent advances and future trends in nanophotonics" aims to give an overview on the latest developments in nanophotonics and its roles in different application domains. Topics of discussion include, but are not limited to, the exploration of new directions of nanophotonic science and technology that enable technological breakthroughs in high-impact areas mainly regarding diffraction elements, detection, imaging, spectroscopy, optical communications, and computing.
An Introduction to the Mathematical Theory of Inverse Problems
This graduate-level textbook introduces the reader to the area of inverse problems, vital to many fields including geophysical exploration, system identification, nondestructive testing, and ultrasonic tomography. It aims to expose the basic notions and difficulties encountered with ill-posed problems, analyzing basic properties of regularization methods for ill-posed problems via several simple analytical and numerical examples. The book also presents three special nonlinear inverse problems in detail: the inverse spectral problem, the inverse problem of electrical impedance tomography (EIT), and the inverse scattering problem. The corresponding direct problems are studied with respect to existence, uniqueness, and continuous dependence on parameters. Ultimately, the text discusses theoretical results as well as numerical procedures for the inverse problems, including many exercises and illustrations to complement coursework in mathematics and engineering. This updated text includes a new chapter on the theory of nonlinear inverse problems in response to the field's growing popularity, as well as a new section on the interior transmission eigenvalue problem which complements the Sturm-Liouville problem and which has received great attention since the previous edition was published.
tp1.3 A continuing inquiry into the Foundations of the Science of Physics
This book, tp1.3, continues a dialog between the three friends, started in tp1.1 and tp1.2, on the foundations of the science of Physics. Having encountered numerous surprises in defining algebras, the friends have elected to continue on to a calculus for three dimensional vectors The friends start by considering whether the set of vectors may harbor a topology. Having found so, they next consider how limits may be defined for such a topology. They quickly arrive at many such: directional limits, omni-directional limits, limits of the first quadrant, limits in the first quadrant, limits in sections, limits along vectorial curves.From each of these limits arises the many definitions of derivatives for the set of vectors. Derivatives may be defined with reference to the underlying field or to the set of vectors itself. Since reference to the underlying field implicates order, these derivatives are called process. Process may occur in a direction, along a curve specified by the field or along a curve defined in set of vectors itself. Derivatives may also be defined with reference to the set of vectors itself, and so relinquish order. These possibilities enable the definition of three other derivatives, namely: divergences, curls, and gradients. These many possibilities are elaborated in their respective contexts. In the context of first quadrant gradients, a definition of the gradient of a vectorial function is defined which becomes a unifying concept for non-process differentiation. Some specific first quadrant results are given. The friends then turn to differentiation in a section. They find such differentiation occupies a central position between quadrant differentiation on the one hand and directional differentiation on the other.Finally the friends produce a table of sums and productsThe friends then turn to vectorial integration, finding they can continue on a path similar to differentiation. First, directional integrals, then process integration along curves. The integration of divergences, curls and gradients are called invergences, incurls, and ingradients respectively. The friends consider integration of functions incorporating step functions where they find interesting results.How, the friends wonder, does one integrate over regions? The answer comes from defining vector measures in the set of vectors. Integration over measurable set then becomes possible. They also pursue results of local integration of local derivatives. And step functions? For the local context, two new step functions are defined: point, and local step functions. In each context results are obtained which are extensions of the fundamental theorem of integral calculus. With step functions, the results are extended to function with a finite number of step discontinuities.With measurable sets comes surfaces. The friends consider derivatives and integrals over the surfaces. They find the development leads to an analysis of the Divergence Theorem.
Journal of Applied Logics. The IfCoLog Journal of Logics and their Applications, Volume 9, Issue 1, January 2022. 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.
Differential Geometry, Differential Equations, and Mathematical Physics
Poisson and Symplectic Structures, Hamiltonian Action, Momentum, and Reduction.- Notes on Tractor Calculi.- Symmetries and Integrals.- Finite Dimensional Dynamics of Evolutionary Equations with Maple.- Critical Phenomena in Darcy and Euler Flows of Real Gases.- Differential Invariants for Flows of Fluids and Gases.
Recent Developments in Algebraic Geometry
Written in celebration of Miles Reid's 70th birthday, this illuminating volume contains 11 papers by leading mathematicians in and around algebraic geometry, broadly related to the themes and interests of Reid's varied career. Just as in Reid's own scientific output, some of the papers give comprehensive accounts of the state of the art of foundational matters, while others give expositions of subject areas or techniques in concrete terms. Reid has been one of the major expositors of algebraic geometry and a great influence on many in this field - this book hopes to inspire a new generation of graduate students and researchers in his tradition.
Interaction of Ionizing Photons with Atomic and Molecular Ions
The interaction of ionising radiation with atomic and/or molecular ions is a fundamental process in nature, with implications for the understanding of many laboratory and astrophysical plasmas. At short wavelengths, the photon-ion interactions lead to inner-shell and multiple electron excitations, leading to demands on appropriate laboratory developments of sources and detectors and requiring advanced theoretical treatments which take into account many-body electron-correlation effects.This book includes a range of papers based on different short wavelength photon sources including recent facility and instrumental developments. Topics include experimental photoabsorption studies with laser-produced plasmas and photoionization of atomic and molecular ions with synchrotron and FEL sources, including modifications of a cylindrical mirror analyzer for high efficiency photoelectron spectroscopy on ion beams. Theoretical investigations include the effects of FEL fluctuations on autoionization line shapes, multiple sequential ionization by intense fs XUV pulses, photoelectron angular distributions for non-resonant two-photon ionization, inner-shell photodetachment of Na- and spin-polarized fluxes from fullerene anions.
Selected Papers from ”Theory of Hadronic Matter under Extreme Conditions”
The book is devoted to the discussion of modern aspects of the theory of hadronic matter under extreme conditions. It consists of 12 selected contributions to the second international workshop on this topic held in fall 2019 at JINR Dubna, Russia. Of particular value are the contributions to lattice gauge theory studies attacking the problem of simulating QCD at finite baryon densities, one of the major challenges at the present time in this field. Another unique aspect is provided by the discussion of puzzling effects that appear in the poduction of hadrons in nuclear collisions, like the horn in the K+/pi+ ratio, which are subject to hydrodynamic and reaction-kinetic modeling of these nonequilibrium phenomena.
New Development of Neutrosophic Probability, Neutrosophic Statistics, Neutrosophic Algebraic Structures, and Neutrosophic Plithogenic Optimizations
This Special Issue puts forward for discussion state-of-the-art papers on new topics related to neutrosophic theories, such as neutrosophic algebraic structures, neutrosophic triplet algebraic structures, neutrosophic extended triplet algebraic structures, neutrosophic algebraic hyperstructures, neutrosophic triplet algebraic hyperstructures, neutrosophic n-ary algebraic structures, neutrosophic n-ary algebraic hyperstructures, refined neutrosophic algebraic structures, refined neutrosophic algebraic hyperstructures, quadruple neutrosophic algebraic structures, refined quadruple neutrosophic algebraic structures, neutrosophic image processing, neutrosophic image classification, neutrosophic computer vision, neutrosophic machine learning, neutrosophic artificial intelligence, neutrosophic data analytics, neutrosophic deep learning, neutrosophic symmetry, and their applications in the real world. This book leads to the further advancement of the neutrosophic and plithogenic theories of NeutroAlgebra and AntiAlgebra, NeutroGeometry and AntiGeometry, Neutrosophic n-SuperHyperGraph (the most general form of graph of today), Neutrosophic Statistics, Plithogenic Logic as a generalization of MultiVariate Logic, Plithogenic Probability and Plithogenic Statistics as a generalization of MultiVariate Probability and Statistics, respectively, and presents their countless applications in our every-day world.
Calculus Made Easy
This Book is a very-simple introduction to the beautiful methods of reckoning which are generally called by the terrifying names of the Differential Calculus and The Integral Calculus.The Contents of the book are as follows .Prologue I. To deliver you from the Preliminary Terrors II. On Different Degrees of Smallness III. On Relative GrowingsV. Simplest Cases V. Next Stage. What to do with Constants VI. Sums, Differences, Products and Quotients VII. Successive Differentiation VIII. When Time Varies IX. Introducing a Useful Dodge X. Geometrical Meaning of DifferentiationXI. Maxima and MinimaXII. Curvature of Curves XIII. Other Useful Dodges XIV. On true Compound Interest and the Law of Organic Growth XV. How to deal with Sines and Cosines XVI. Partial Differentiation XVII. Integration XVIII. Integrating as the Reverse of Differentiating XIX. On Finding Areas by Integrating XX. Dodges, Pitfalls, and Triumphs XXI. Finding some Solutions Table of Standard Forms
Wavelet Based Approximation Schemes for Singular Integral Equations
Many mathematical problems in science and engineering are defined by ordinary or partial differential equations with appropriate initial-boundary conditions. Among the various methods, boundary integral equation method (BIEM) is probably the most effective. It's main advantage is that it changes a problem from its formulation in terms of unbounded differential operator to one for an integral/integro-differential operator, which makes the problem tractable from the analytical or numerical point of view. Basically, the review/study of the problem is shifted to a boundary (a relatively smaller domain), where it gives rise to integral equations defined over a suitable function space. Integral equations with singular kernels areamong the most important classes in the fields of elasticity, fluid mechanics, electromagnetics and other domains in applied science and engineering. With the advancesin computer technology, numerical simulations have become important tools in science and engineering. Several methods have been developed in numerical analysis for equations in mathematical models of applied sciences. Widely used methods include: Finite Difference Method (FDM), Finite Element Method (FEM), Finite Volume Method (FVM) and Galerkin Method (GM). Unfortunately, none of these are versatile. Each has merits and limitations. For example, the widely used FDM and FEM suffers from difficulties in problem solving when rapid changes appear in singularities. Even with the modern computing machines, analysis of shock-wave or crack propagations in three dimensional solids by the existing classical numerical schemes is challenging (computational time/memory requirements). Therefore, with the availability of faster computing machines, research into the development of new efficient schemes for approximate solutions/numerical simulations is an ongoing parallel activity. Numerical methods based on wavelet basis (multiresolution analysis) may be regarded as a confluence of widely used numerical schemes based on Finite Difference Method, Finite Element Method, Galerkin Method, etc. The objective of this monograph is to deal with numerical techniques to obtain (multiscale) approximate solutions in wavelet basis of different types of integral equations with kernels involving varieties of singularities appearing in the field of elasticity, fluid mechanics, electromagnetics and many other domains in applied science and engineering.
Theoretical and Computational Research in Various Scheduling Models
Nine manuscripts were published in this Special Issue on "Theoretical and Computational Research in Various Scheduling Models, 2021" of the MDPI Mathematics journal, covering a wide range of topics connected to the theory and applications of various scheduling models and their extensions/generalizations. These topics include a road network maintenance project, cost reduction of the subcontracted resources, a variant of the relocation problem, a network of activities with generally distributed durations through a Markov chain, idea on how to improve the return loading rate problem by integrating the sub-tour reversal approach with the method of the theory of constraints, an extended solution method for optimizing the bi-objective no-idle permutation flowshop scheduling problem, the burn-in (B/I) procedure, the Pareto-scheduling problem with two competing agents, and three preemptive Pareto-scheduling problems with two competing agents, among others. We hope that the book will be of interest to those working in the area of various scheduling problems and provide a bridge to facilitate the interaction between researchers and practitioners in scheduling questions. Although discrete mathematics is a common method to solve scheduling problems, the further development of this method is limited due to the lack of general principles, which poses a major challenge in this research field.
Differential Equation Models in Applied Mathematics
The present book contains the articles published in the Special Issue "Differential Equation Models in Applied Mathematics: Theoretical and Numerical Challenges" of the MDPI journal Mathematics. The Special Issue aimed to highlight old and new challenges in the formulation, solution, understanding, and interpretation of models of differential equations (DEs) in different real world applications. The technical topics covered in the seven articles published in this book include: asymptotic properties of high order nonlinear DEs, analysis of backward bifurcation, and stability analysis of fractional-order differential systems. Models oriented to real applications consider the chemotactic between cell species, the mechanism of on-off intermittency in food chain models, and the occurrence of hysteresis in marketing. Numerical aspects deal with the preservation of mass and positivity and the efficient solution of Boundary Value Problems (BVPs) for optimal control problems. I hope that this collection will be useful for those working in the area of modelling real-word applications through differential equations and those who care about an accurate numerical approximation of their solutions. The reading is also addressed to those willing to become familiar with differential equations which, due to their predictive abilities, represent the main mathematical tool for applying scenario analysis to our changing world.
