The effect of heat and mass transfer on MHD flow in channels and ducts
Transport phenomena involving the combined influence of thermal and concentration buoyancy are often encountered in many engineering systems and natural environments. Combined heat and mass transfer problems with chemical reactions are important in many processes and received a considerable amount of attention in recent years. Obviously, an understanding of this transport process is desirable in order to effectively control the overall transport characteristics. In this context, we make an attempt to investigate the effect of dissipation, the Soret effect, and radiation on the unsteady double diffusive flow of a viscous and electrically conducting fluid through a porous medium in a vertical channel. Also, investigated the Heat and Mass transfer of a viscous fluid with radiation effect in channels/ducts. We discuss the effect of radiation, thermo-diffusion, dissipation, and heat sources on the convective heat and mass transfer flow of a viscous fluid through a porous medium in a rectangular duct.
Scientific Data Analysis with R
This book is intended for students, researchers, and professionals eager to harness the combined power of biostatistics, data science, and the R programming language while gathering vital statistical knowledge needed for cutting-edge scientists in all fields.
Application of Statistical Computing to Statistical Learning
The study here is about supervised learning, an aspect of statistical learning. We identified prediction as the mainstay of supervised learning, and further noted that when the outcome of prediction is a categorical variable, classification obtains, otherwise what we have is regression, meaning that the prediction outcome is a continuous variable.A distinguishing aspect of this work is our ability to show both mathematically with a proof, and practically with some real-world datasets, that regression tools can be used as veritable tools for classification.
Mathematical Analysis for Economists
This book provides economics students with a comprehensive foundation in mathematical analysis, focusing on key concepts necessary for advanced economic models and quantitative methods. Divided into five chapters, it covers essential topics: numerical series, numeric functions of two variables, double integrals, improper integrals, and differential equations. Each chapter is designed with exercises and practical applications relevant to economics, enabling students to build both theoretical understanding and applied skills. Through this approach, students gain a mathematical toolkit vital for advanced studies and future careers in economics.
Text Book of Practical Analytical Chemistry
Experimental Book of Pharmaceutical Analysis enables students to gain fundamental knowledge of the vital concepts, techniques, and applications of the chemical analysis of pharmaceutical ingredients, final pharmaceutical products, and drug substances in biological fluids. A unique emphasis on pharmaceutical laboratory practices, such as sample preparation and separation techniques, provides an efficient and practical educational framework for undergraduate studies in areas such as pharmaceutical sciences, analytical chemistry, and forensic analysis. Suitable for foundational courses, this essential undergraduate text introduces the common analytical methods used in quantitative and qualitative chemical analysis of pharmaceuticals.
Stochastic Analysis For Some Non-Linear Epidemic Models
Stochastic calculus has emerged as a robust mathematical framework for modeling complex biological systems characterized by inherent randomness and uncertainty. Unlike traditional deterministic models, which often fail to capture the variability observed in biological processes, stochastic calculus allows for directly incorporating noise and random fluctuations into the modeling equations. This approach is efficient in areas such as population dynamics, gene expression, neural activity, and the spread of infectious diseases, where biological systems are influenced by numerous random factors at both the microscopic and macroscopic levels. By utilizing tools such as stochastic differential equations (SDEs) and the It繫 calculus, researchers can describe the temporal evolution of biological systems in a manner that accounts for both the deterministic trends and stochastic perturbations.
Theory and Applications of Analytical Integration Methods
Dive into a captivating journey through the complex world of integral calculus with this first volume, "Theory and Applications of Analytical Integration Methods: From Mathematical Foundations to Practical Solutions", the first tome of a two-volume series. This first volume delves deeply into analytical integration methods, while the second volume focuses on numerical methods and their implementation in Python. Through nine carefully structured chapters, explore the fundamentals of integral calculus and dive into its numerous practical applications in geometry, statistics, electricity, thermochemistry, and mechanics. Designed for a broad audience, whether you're a novice or an expert, this book offers a comprehensive and accessible approach to mastering integral calculus with little to no external assistance. Each chapter is enriched with clear examples and practical exercises, accompanied by detailed solutions to enhance understanding. The great strength of this series lies in the rigorous validation of results obtained by analytical resolution against those obtained using numerical methods, which are further confirmed by computer-generated results.
Dynamic Modelling Related to Mathematical Applications
This book provides an introduction to the concepts and methods of dynamic modeling related to mathematical applications and its applications to population dynamics and phylogenetics. It offers an overview of topics such as history, data analysis tools, equations, and various techniques used to solve differential, integral, linear, and discrete time dynamic models. The chapters also include case studies and examples of data analysis and graphical methods to illustrate simulation methods and the application of dynamic model characteristics. The underlying mathematical concepts and principles are discussed in detail to explain application to real-world problems.This book is written with the intention of providing an overview of dynamic modeling and its related mathematical applications, which would benefit students and researchers in mathematics, biology, and engineering.
Random Number Generators on Computers
This monograph proves that any finite random number sequence is represented by the multiplicative congruential (MC) way. It also shows that an MC random number generator (d, z) formed by the modulus d and the multiplier z should be selected by new regular simplex criteria to give random numbers an excellent disguise of independence. The new criteria prove further that excellent subgenerators (d1, z1) and (d2, z2) with coprime odd submoduli d1 and d2 form an excellent combined generator (d = d1d2, z) with high probability by Sunzi's theorem of the 5th-6th centuries (China), contrasting the fact that such combinations could never be found with MC subgenerators selected in the 20th-century criteria. Further, a combined MC generator (d = d1d2, z) of new criteria readily realizes periods of 252 or larger, requiring only fast double-precision arithmetic by powerful Sunzi's theorem. We also obtain MC random numbers distributed on spatial lattices, say two-dimensional 4000 by 4000 lattices which may be tori, with little pair correlations of random numbers across the nearest neighbors. Thus, we evade the problems raised by Ferrenberg, Landau, and Wong.
Pencils of matrices and their applications
The present book is an important contribution of matrix theory and its applications. It consists of an introduction and (04) chapters where we review certain basic definitions also we introduce the concept of invariant polynomials. This book is dedicated to the application of pencils to solve implicit differential systems.
Calculus
What knowledge should a calculus textbook cover? Are we able to tell the goals of learning on top of the content from the outline of the textbook? After every abstruse definition and theory, if there's only one or two simple demonstrations, what then, is the root cause for students' inability to solve those difficult practices, a lack of practice or the unfamiliarity of different practice variations? If there's an exam starting minutes away, what content can be remembered from a closed textbook? There are five highlights in this textbook: First of all, readers can be aware of the learning goals of each chapter from the outline, allowing beginners to calculus to have clear understanding of the textbook's structure.Secondly, before sample practices in each chapter, classic question variations are outlined with steps in solutions. Hence, after practicing, readers will be able to fully grasp the concepts and variation through steps of the solutions.Thirdly, the book contains more than 2,000 samples and each sample is demonstrated with the most thorough solution steps. Hence, readers will not find themselves confused with skipped steps.Fourthly, in hopes of allowing readers to understand the book as a whole, including relationships between chapters and significance in specific chapters, I've written the textbook as plain and straight-forward as possible. For instance, knowing where and how L'H繫pital's rule will be used in later chapters.Finally, in contrast with the simple explanations, each sample question is answered with great rigor and accuracy. Across all sample practices in the book, I've only used "Let", "Then", "Since", "Thus", and "Such that" to keep explanations simple and consistent. With all the above mentioned, I hope to present the most detailed context of calculus to all the readers.
On primes, sum of numbers, Mandelbrot fractal and theory of relativity
The book deals with the linear position of prime numbers, with the simultaneous chaotic nature of their distribution. It also derives some recursive formulas of prime numbers of nested square roots and shows their connection with the Pi. It also presents a new approach to the problem of the negative sum of natural numbers. The conclusion presents considerations on the special theory of relativity without the use of time and velocity.
The Theory of Countable Borel Equivalence Relations
The theory of definable equivalence relations has been a vibrant area of research in descriptive set theory for the past three decades. It serves as a foundation of a theory of complexity of classification problems in mathematics and is further motivated by the study of group actions in a descriptive, topological, or measure-theoretic context. A key part of this theory is concerned with the structure of countable Borel equivalence relations. These are exactly the equivalence relations generated by Borel actions of countable discrete groups and this introduces important connections with group theory, dynamical systems, and operator algebras. This text surveys the state of the art in the theory of countable Borel equivalence relations and delineates its future directions and challenges. It gives beginning graduate students and researchers a bird's-eye view of the subject, with detailed references to the extensive literature provided for further study.
Probability Theory, an Analytic View
The third edition of this highly regarded text provides a rigorous, yet entertaining, introduction to probability theory and the analytic ideas and tools on which the modern theory relies. The main changes are the inclusion of the Gaussian isoperimetric inequality plus many improvements and clarifications throughout the text. With more than 750 exercises, it is ideal for first-year graduate students with a good grasp of undergraduate probability theory and analysis. Starting with results about independent random variables, the author introduces weak convergence of measures and its application to the central limit theorem, and infinitely divisible laws and their associated stochastic processes. Conditional expectation and martingales follow before the context shifts to infinite dimensions, where Gaussian measures and weak convergence of measures are studied. The remainder is devoted to the mutually beneficial connection between probability theory and partial differential equations, culminating in an explanation of the relationship of Brownian motion to classical potential theory.
The Art of Working with the Mathieu Group M24
The Leech lattice Λ, the Conway group ∙O, and the Monster group M are immensely famous structures. They each grow out of the Mathieu group M24 and its underlying combinatorial structure, and play an important role in various branches of mathematics and in theoretical physics. Written by an expert in the field, this book provides a new generation of mathematicians with the intimate knowledge of M24 needed to understand these beautiful objects, and many others. It starts by exploring Steiner systems, before introducing the Miracle Octad Generator (MOG) as a device for working with the Steiner system S(5,8,24). Emphasizing how theoretical and computational approaches complement one another, the author describes how familiarity with M24 leads to the concept of 'symmetric generation' of groups. The final chapter brings together the various strands of the book to produce a nested chain of groups culminating in the largest Conway simple group Co1.
The Essential George Boole
The Essential George Boole: Logic, Love, and Legacy is a captivating biography that explores the extraordinary life of George Boole, a self-taught English mathematician whose groundbreaking work laid the foundation for the digital age. Despite his humble beginnings and lack of formal education, Boole's passion for learning and his relentless pursuit of knowledge led him to master multiple languages, explore various scientific disciplines and ultimately revolutionise the field of mathematics.This book not only showcases Boole's intellectual brilliance but also sheds light on his personal life, including his marriage to the remarkable Mary Everest, who hailed from a distinguished family. Together, they raised five talented daughters who left their own mark on the world in fields ranging from chemistry and mathematics to literature and medicine, creating a lasting legacy that spans generations.Through a compelling narrative, the authors paint a vivid picture of Boole's life, from his early struggles to support his family to his rise as a respected professor and his untimely death at the height of his career. The Essential George Boole: Logic, Love, and Legacy is a testament to the power of perseverance, the beauty of the human mind, and the enduring impact one person can have on the world.
Differential Geometry
This Special Issue presents recent developments in the field of structures on manifolds and their submanifolds. This volume covers a vast range of topics, including twister product Hermitian manifold, Legendrian warped product submanifold, Bertrand curve pair, CR-slant warped product, RW spacetime, Li-Yao-type gradient, Ricci-Yamabe solutions, etc., thus stimulating further research in this area.
Mathematics teaching-learning process
The proposed system of activities helps the development of calculus skills in the basic addition exercises with surplus in third grade students. It is necessary to improve the quality of the teaching-learning process of mathematics in elementary school. The diagnosis carried out revealed that the greatest difficulties are: lack of good memorization, skills, speed and accuracy.
Dynamic Modeling and Simulation for Control Systems, 2nd Edition
This special issue contains all the articles published in the Special Issue "Dynamic Modeling and Simulation for Control Systems, Second Edition" from the MDPI Mathematics journal. This Special Issue is a follow-up to our first successful edition. It offers researchers and practitioners a platform to explore topics related to the dynamic modeling, simulation, and optimization of control systems in various engineering fields. The aim is to cover vital aspects of optimizing the dynamic behavior of physical systems using algorithms and artificial intelligence. The applications span diverse areas such as astronautics, aerospace, avionics, robotics, manufacturing systems, mechanical engineering, power energy, materials technology, and neurorehabilitation. We hope this Special Issue will make a significant contribution to the research on modeling, simulation, and optimization techniques for dynamic control systems.
Database Systems for Advanced Applications
The seven-volume set LNCS 14850-14856 constitutes the proceedings of the 29th International Conference on Database Systems for Advanced Applications, DASFAA 2024, held in Gifu, Japan, in July 2024. The total of 147 full papers, along with 85 short papers, presented together in this seven-volume set was carefully reviewed and selected from 722 submissions. Additionally, 14 industrial papers, 18 demo papers and 6 tutorials are included. The conference presents papers on subjects such as: Part I: Spatial and temporal data; database core technology; federated learning. Part II: Machine learning; text processing. Part III: Recommendation; multi-media. Part IV: Privacy and security; knowledge base and graphs. Part V: Natural language processing; large language model; time series and stream data. Part VI: Graph and network; hardware acceleration. Part VII: Emerging application; industry papers; demo papers.
Reviewing Knowledge
The book is a collection of critical reviews that are essential for teacher training. The texts in this collection deal with themes that are important to the academic world. They are dialogues with theories and knowledge constructed by different authors with a view to contributing to the training of teachers in this century and to innovating their pedagogical praxis. In this work, we bring to the focus of the dialogue texts such as: 'Beyond Abyssal Thinking: From Global Lines to an Ecology of Knowledges' by Professor Boaventura de Souza; notes on 'Conscientisation: Theory and Practice of Liberation: An Introduction to the Thought of Paulo Freire; Edgar Morin's 'Seven Knowledges Necessary for the Education of the Future' and finally a contextualisation of teacher training: 'Teacher Training in the Context of the Pedagogical Proposals of Rudolf Steiner (Waldorf Pedagogy), Maria Montessori and the Escola da Ponte Experience' by Evelaine C. dos Santos.
Transactions on Large-Scale Data- And Knowledge-Centered Systems LVII
The LNCS journal Transactions on Large-scale Data and Knowledge-centered Systems focuses on data management, knowledge discovery, and knowledge processing, which are core and hot topics in computer science. Since the 1990s, the Internet has become the main driving force behind application development in all domains. An increase in the demand for resource sharing (e.g., computing resources, services, metadata, data sources) across different sites connected through networks has led to an evolution of data- and knowledge-management systems from centralized systems to decentralized systems enabling large-scale distributed applications providing high scalability. This, the 57th issue of Transactions on Large-Scale Data and Knowledge-Centered Systems, contains five fully revised selected regular papers. Topics covered include leveraging machine learning for effective data management, access control models, reciprocal authorizations, Internet of Things, digital forensics, code similarity search, volunteered geographic information, and spatial data quality.
Principles and Applications of Numerical Integration Methods
Dive into a captivating journey through the complex world of integral calculus with this second volume, "Analytical Integration Methods - Courses and Exercises", part of a two-volume series. This tome focuses on numerical integration methods and their implementation in Python. It follows the first volume which explores analytical methods in integral calculus. Together, these two volumes offer a comprehensive approach to mastering integral calculus. Designed for a broad audience, whether you're a novice or an expert, this book provides a thorough and accessible approach to mastering numerical methods with little to no external assistance. It delves deeply into methods such as rectangles, midpoint, trapezoids, Simpson's, Weddle's, and Gauss's, while emphasizing precision and error management. Each chapter is enriched with clear examples and practical exercises, accompanied by detailed solutions to enhance understanding. The great strength of this series lies in the rigorous validation of results obtained by analytical resolution against those obtained using numerical methods, which are further confirmed by computer-generated results.
Fuzzy Mathematics, Graphs, and Similarity Measures
Fuzzy Mathematics, Graphs, and Similarity Measures provides a solid foundation in core analytical tracks of mathematics of uncertainty, from fuzzy mathematics to graphs and similarity measures with applications in a range of timely cases studies and world challenges. Following a full grounding in fuzzy graph indices, connectivity in fuzzy graph structures, lattice isomorphisms, and similarity measures, the book applies these models in analyzing world challenges, from human trafficking to modern slavery, global poverty, global hunger, homelessness, biodiversity, extinction, terrorism and bioterrorism, pandemics, and climate change. Connections and constructive steps forward are tied throughout to UN Sustainable Development Goals (SDGs). The authors demonstrate and instruct readers in applying techniques from mathematics of uncertainty in examining issues where accurate data is impossible to obtain. In addition to a diverse range of cases studies, exercises reinforce key concepts in each chapter, and an online instructor's manual supports teaching across a range of course contexts.
Topics in Infinite Group Theory
This book gives an advanced overview of several topics in infinite group theory. It can also be considered as a rigorous introduction to combinatorial and geometric group theory. The philosophy of the book is to describe the interaction between these two important parts of infinite group theory. In this line of thought, several theorems are proved multiple times with different methods either purely combinatorial or purely geometric while others are shown by a combination of arguments from both perspectives. The first part of the book deals with Nielsen methods and introduces the reader to results and examples that are helpful to understand the following parts. The second part focuses on covering spaces and fundamental groups, including covering space proofs of group theoretic results. The third part deals with the theory of hyperbolic groups. The subjects are illustrated and described by prominent examples and an outlook on solved and unsolved problems. New edition now includes the topics on universal free groups, quasiconvex subgroups and hyperbolic groups, and also Stallings foldings and subgroups of free groups. New results on groups of F-types are added.
Introduction to Financial Mathematics
The second edition of this successful and widely recognized textbook again focuses on discrete topics. The author recognizes two distinct paths of study and careers of actuarial science and financial engineering. This text can be very useful as a common core for both. Therefore, there is substantial material in Introduction to Financial Mathematics, Second Edition on the theory of interest (the first half of the book), as well as the probabilistic background necessary for the study of portfolio optimization and derivative valuation (the second half). A course in multivariable calculus is not required.The material in the first two chapters should go a long way toward helping students prepare for the Financial Mathematics (FM) actuarial exam. Also, the discrete material will reveal how beneficial it is for the students to know more about loans in their personal financial lives.The notable changes and updates to this edition are itemized in the Preface, but overall, the presentation has been made more efficient. One example is the chapter on discrete probability, which is rather unique in its emphasis on giving the deterministic problems studied earlier a probabilistic context. The section on Markov chains, which is not essential to the development, has been scaled down. Sample spaces and probability measures, random variables and distributions, expectation, conditional probability, independence, and estimation all follow.Optimal portfolio selection coverage is reorganized and the section on the practicalities of stock transactions has been revised. Market portfolio and Capital Market Theory coverage is expanded. New sections on Swaps and Value-at-Risk have been added. This book, like the first edition, was written so that the print edition could stand alone. At times we simplify complicated algebraic expressions, or solve systems of linear equations, or numerically solve non-linear equations. Also, some attention is given to the use of computer simulation to approximate solutions to problems.
Risk Factors & Prevention of Coronary Heart Disease
"Coronary heart disease (CHD) is a leading cause of morbidity and mortality worldwide. This study aims to investigate the demographic and clinical characteristics of patients with CHD at ESI Hospital, Maniktala, Kolkata, and assess the prevalence of risk factors for CHD. Additionally, it explores the perspectives of healthcare professionals and policymakers on CHD prevention, identifies challenges and barriers in CHD management, and proposes evidence-based recommendations for effective prevention strategies."
Advanced Mathematics for Science and Technology
This book presents the fundamental concepts essential to the second-year mathematics program in science and technology. The first chapter thoroughly explores integral calculus, including the Riemann integral, double and triple integrals, and their applications in calculating areas and volumes. The second chapter addresses improper integrals and their properties. The third chapter is dedicated to ordinary differential equations, focusing on linear differential equations of the first and second order, as well as partial differential equations. The fourth chapter delves into numerical series, sequences and series of functions, power series, and Fourier series. In the fifth chapter, we introduce the Fourier transform and its properties. The sixth chapter covers the Laplace transform, its properties, and its application in solving differential equations. Each chapter is accompanied by a series of exercises designed to reinforce the understanding of the presented concepts.
Discretization in Differential Equations and Enclosures
No detailed description available for "Discretization in Differential Equations and Enclosures".
Geometrodynamics of Gauge Fields
No detailed description available for "Geometrodynamics of Gauge Fields".
Quadrature Formulae
No detailed description available for "Quadrature Formulae".
The Statistical Analysis of Small Data Sets
We live in the era of big data. However, small data sets are still common for ethical, financial, or practical reasons. Small sample sizes can cause researchers to seek out the most powerful methods to analyse their data, but they may also be wary that some methodologies and assumptions may not be appropriate when samples are small. The book offers advice on the statistical analysis of small data sets for various designs and levels of measurement, helping researchers to analyse such data sets, but also to evaluate and interpret others' analyses. The book discusses the potential challenges associated with a small sample, as well as the ways in which these challenges can be mitigated. General topics with strong relevance to small sample sizes such as meta-analysis, sequential and adaptive designs, and multiple testing are introduced. While the focus is on hypothesis tests and confidence intervals, Bayesian analyses are also covered. Code written in the statistical software R is presented to carry out the proposed methods, many of which are not limited to use on small data sets, and the book also discusses approaches to computing the power or the necessary sample size, respectively.
Solution Curve For Control Systems on Lie Groups
In the context of Lie groups, Control Theory is primarily concerned with the study of invariant, linear, bilinear and affine control systems. For invariant systems - considering that the control functions are piecewise constant - the solutions of the system has a well known and good description. This brings us to the first objective of this work: to give an explicit description of the solution curve for the other systems under the assumption that the linear vector fields commute. These solutions are obtained as the integral curve of a convenient invariant vector field on a semidirect product of a Lie group with an Euclidean space. In particular, we consider the case where the derivations associated to the linear vector fields are inner (which occurs, for example, in every semi simple Lie algebra), in which case the solutions are described in a considerably simpler and more elegant way. Thenceforth, our achievements are applied to obtain new propositions. The results range from expressions that relate the controllability of linear/affine control systems with associated invariant ones to the study of system semiconjugation by Lie group homomorphisms and properties of stability sets.
Introduction to Transfer Learning
Transfer learning is one of the most important technologies in the era of artificial intelligence and deep learning. It seeks to leverage existing knowledge by transferring it to another, new domain. Over the years, a number of relevant topics have attracted the interest of the research and application community: transfer learning, pre-training and fine-tuning, domain adaptation, domain generalization, and meta-learning. This book offers a comprehensive tutorial on an overview of transfer learning, introducing new researchers in this area to both classic and more recent algorithms. Most importantly, it takes a "student's" perspective to introduce all the concepts, theories, algorithms, and applications, allowing readers to quickly and easily enter this area. Accompanying the book, detailed code implementations are provided to better illustrate the core ideas of several important algorithms, presenting good examples for practice.
Advanced Techniques in Control Charting
The book Advanced Techniques in Control Charting for Process Monitoring offers a timely and insightful look into the contemporary uses of control charts. It delivers a comprehensive analysis of advanced methods, focusing on their impact in optimizing process control, improving quality, and increasing efficiency across multiple industries. Covering topics such as the integration of machine learning algorithms and multivariate control charts, this book presents a diverse range of innovative techniques that are revolutionizing how processes are monitored and managed in modern industrial settings.
The Statistical Analysis of Small Data Sets
We live in the era of big data. However, small data sets are still common for ethical, financial, or practical reasons. Small sample sizes can cause researchers to seek out the most powerful methods to analyse their data, but they may also be wary that some methodologies and assumptions may not be appropriate when samples are small. The book offers advice on the statistical analysis of small data sets for various designs and levels of measurement, helping researchers to analyse such data sets, but also to evaluate and interpret others' analyses. The book discusses the potential challenges associated with a small sample, as well as the ways in which these challenges can be mitigated. General topics with strong relevance to small sample sizes such as meta-analysis, sequential and adaptive designs, and multiple testing are introduced. While the focus is on hypothesis tests and confidence intervals, Bayesian analyses are also covered. Code written in the statistical software R is presented to carry out the proposed methods, many of which are not limited to use on small data sets, and the book also discusses approaches to computing the power or the necessary sample size, respectively.
Reverse Dynamic Inequalities on Time Scales
Inequalities lie at the heart of the mathematical analysis which is a major and important branch of mathematics. Throughout the history, many researchers discovered agreat number of inequalities that are very useful in many fields of mathematics. Thestudy of inequalities became very popular in the twentieth century specially afterthe publishing of the pioneering book. In 1988, Stephan Hilger introduced in his PhD thesis a new theory, the theoryof time scales, which builds bridges between continuous and discrete mathematics.The main idea is to prove a result for a dynamic inequality where the domain of theunknown function is a so-called time scale T, which is defined as an arbitrary closedsubset of the real numbers R, to avoid proving results twice, once in the continuouscase which leads to an integral inequality and once again on a discrete case whichleads to a discrete inequality.Recently, the study of dynamic inequalities on time scales has attracted the attention of many mathematicians. One of the applications of this kind of inequalitiesis to study the behavior of solutions of dynamic equations on time scales.
Probabilistic Spiking Neuronal Nets
This book provides a self-contained introduction to a new class of stochastic models for systems of spiking neurons. These systems have a large number of interacting components, each one evolving as a stochastic process with a memory of variable length. Several mathematical tools are put to use, such as Markov chains, stochastic chains having memory of variable length, point processes having stochastic intensity, Hawkes processes, random graphs, mean field limits, perfect sampling algorithms, the Context algorithm, and statistical model selection.The book's focus on mathematically tractable objects distinguishes it from other texts on theoretical neuroscience. The biological complexity of neurons is not ignored, but reduced to some of its main features, such as the intrinsic randomness of neuronal dynamics. This reduction in complexity aims at explaining and reproducing statistical regularities and collective phenomena that are observed in experimental data, an approach that leads to mathematically rigorous results. With an emphasis on a constructive and algorithmic point of view, this book is directed towards mathematicians interested in learning about stochastic network models and their neurobiological underpinning, and neuroscientists interested in learning how to build and prove results with mathematical models that relate to actual experimental settings.
Dynamics of Circle Mappings
This book explores recent developments in the dynamics of invertible circle maps, a rich and captivating topic in one-dimensional dynamics. It focuses on two main classes of invertible dynamical systems on the circle: global diffeomorphisms and smooth homeomorphisms with critical points. The latter is the book's core, reflecting the authors' recent research interests.Organized into four parts and 14 chapters, the content covers rigid rotations, circle homeomorphisms, and the concept of rotation number in the first part. The second part delves into circle diffeomorphisms, presenting classical results. The third part introduces multicritical circle maps--smooth homeomorphisms of the circle with a finite number of critical points. The fourth and final part centers on renormalization theory, analyzing the fine geometric structure of orbits of multicritical circle maps. Complete proofs for several fundamental results in circle dynamics are provided throughout. The book concludes with a list of open questions.Primarily intended for graduate students and young researchers in dynamical systems, this book is also suitable for mathematicians from other fields with an interest in the subject. Prerequisites include familiarity with the content of a standard graduate course in real analysis, along with some understanding of ergodic theory and dynamical systems. Basic knowledge of complex analysis is needed for specific chapters.
Lectures on Lie Algebras
No detailed description available for "Lectures on Lie Algebras".
Fuzzy Soft Ternary Γ-Semirings
Fuzzy soft ternary gamma semirings are an advanced mathematical structure that combines elements from fuzzy logic, soft set theory, ternary operations, and gamma semirings. This book provides information on Fuzzy Soft Quasi TΓ-Ideals in Fuzzy Soft TΓ-Semirings, On Fuzzy Soft Interior TΓ-Ideals, Fuzzy Soft Radicals in Fuzzy Soft TΓ-Semirings, Fuzzy Soft TΓ-Homomorphism in TΓ-Semirings. Each topic has been started with introductory part and developed gradually up to the standard form.
The Philosophy of Penelope Maddy
This volume features more than 20 essays that explore the work of one of the most important contemporary philosophers of mathematics. It will help readers to better appreciate this significant and prolific philosopher. Within philosophy of mathematics, Penelope Maddy initially advocated realism. She then went on to advance naturalism. Both of her positions became very influential in the field, along with her other work in the philosophy of logic. The contributors comment on and otherwise engage with Maddy's work. They also weigh in on the state of set theory and its philosophy, the philosophy and history of logic, naturalism, skepticism, and the myriad other areas to which Maddy left her mark. Overall, coverage traces her influence on these various ideas over the years. It will also help readers to better understand how philosophers working at the forefront of these areas see these concepts today. These essays will be essential reading for the wide group of philosophers working in these different areas as well as graduate students studying philosophy of mathematics and logic and the other related issues to which Maddy has contributed. The volume will also appeal to logicians and set theorists in general, as well as to philosophers working in analytic philosophy more widely, as well as to those working in the history of philosophy.
