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An Introduction to the Distance Laplacian Spectra of Graphs
In this book, we determine the distance Laplacian spectra of graphs obtained by various graph operations.We first obtain the distance Laplacian spectrum of the join of two graphs in terms of adjacency spectra. Then we obtain the distance Laplacian spectrum of the join of two graphs in which one of the graphs is a union of two graphs. Finally, we obtain the distance Laplacian spectrum of the generalized join of graphs. We then find the universal adjacency spectra of the join of two regular graphs with distinct degrees and the join of two regular graphs in which of the graphs is a union of two regular graphs in terms of adjacency spectra of the constituent graphs and an auxiliary matrix. We obtain the distance Laplacian spectrum of Indu-Bala product of graphs in terms of their Laplacian spectra. We then obtain the distance signless Laplacian spectrum of Indu-Bala product of graphs in terms of their signless Laplacian spectra. Finally, we prove that the distance energy of the complete split graph always increases when an edge is deleted from it.
Examining the Challenges and New Methods
The importance and necessity of evaluation in the process of educational activities can be examined from two perspectives. The first point of view is related to the planner or teacher. In fact, in planning teaching and making decisions during educational activities, in order to obtain reliable information on the preparation and academic progress of learners and the effectiveness of their classroom activities through evaluation, the teacher finds information and awareness about three categories. These categories include: A) Problems and deficiencies in the elements of the educational plan (goals, content, methods, materials and educational tools); B) The level of academic progress of learners and their preparation for further education and C) The efficiency of teaching and the adequacy of the tools used in measuring the academic progress of learners. The second point of view is related to learners. In such a way that through evaluation, learners are encouraged to develop their positive aspects and solve their educational deficiencies with the help and guidance of the teacher, while being aware of the positive and negative aspects of their performance in learning.
Abstract Algebra
Abstract algebra is the study of algebraic structures like groups, rings and fields. This book provides an account of the theoretical foundations including applications to Galois Theory, Algebraic Geometry and Representation Theory. It implements the pedagogic approach to conveying algebra from the perspective of rings. The 3rd edition provides a revised and extended versions of the chapters on Algebraic Cryptography and Geometric Group Theory.
Scalar Conservation Laws
This book are notes prepared for the PhD courses that the author has been teaching during the last 10 years. The material available in the already existing literature (papers and essays) has been collected in this unique text, presenting the results with all the details for the reader's convenience, fixing a unified notation, and providing a consistent framework for the subject. These notes cover many of the arguments that usually can be found in high level essays, where the proofs are simply sketched, and in papers, which are not easily available and not always self-contained.This book is intended for1. PhD students in Mathematics, Physics and Mechanical Engineering in order to learn the basic features of nonlinear scalar equations, 2. researchers interested in nonlinear hyperbolic PDEs in order to learn the details behind some known and deep results on nonlinear scalar equations, 3. teachers of courses on nonlinear PDEs.The readers are expected to know the basic measure theory and Sobolev spaces.
Advances in Neural Networks - Isnn 2024
This volume constitutes the refereed proceedings of the 18th International Symposium on Neural Networks, ISNN 2024, held in Weihai, China, during 11-14, July 2024. The 59 full papers were carefully reviewed and selected from 82 submission. They are categorized in the following sections: Optimization Algorithms; Adversarial Learning, Transfer Learning, and Deep Learning; Signal, Image, and Video Processing; Modeling, Analysis, and Implementation of Neural Networks; Control Systems, Robotics, and Autonomous Driving; Fault Diagnosis and Intelligent Industry & Bio-signal, Bioinformatics, and Biomedical Engineering.
Fixed Point Results on Various Metric Spaces with Applications
This book "Fixed Point Results on Various Metric Spaces with Applications" aims to present advanced results in fixed point theory that expand upon, enhance, and generalize classical and recent findings in this field. It also explores various research avenues within the metric fixed-point theory. It offers opportunities for more investigation and serves as a readily available reservoir of information. This book is suitable for young researchers interested in pursuing research in fixed-point theory. It provides the latest advancements in the field, offering new techniques for proving the existence of various types of fixed points, such as fixed points, fixed interval circles, fixed discs, coincidence points, common fixed points, coupled common fixed points, quadruple fixed points, quadruple coincidence points and common quadruple fixed points. These tech In addition to conventional applications, it provides innovative applications that can be used to solve integral equations and Homotopy Theory. The book is both self-contained and unified, making it an invaluable resource for researchers seeking innovative ideas. It will be a valuable addition to the library.
Fixed Point Theorem in Different Spaces
The development of computers has led to the emergence of numerous scientific and technological fields of study. At the same time as it has replaced and replicated the uses of mathematics in science and technology, it has also highlighted a lot of issues with mathematical theories. Functional analysis and topology are closely linked topics that were discussed before. The fixed point theorem has emerged as a key instrument for research in both mathematics and other branches of management science and technology. The purpose of our research is to illuminate the novel features of fixed point theorems in various spaces with regard to applications. Our study aims to uncover innovative aspects of Banach fixed point theorems or Banach contraction theorem in different metric spaces such as TVS-Cone metric space, c distance in cone metric space, c -complete complex valued metric space, complex valued b-metric space and Modular metric space . Henceforth, it has become a very important study for correlating and coordinating various aspects of fixed point theorems.
New Directions in Term Logic
The systematic account of deductive reasoning and the development of a formal logic to reveal the principles of such reasoning began with Aristotle's syllogistic. It was a term logic, a logic that dominated the field until the rise of modern predicate logic at the end of the Nineteenth century. That system quickly supplanted the old logic of terms. However, in the middle of the Twentieth century Fred Sommers took up the challenge to build a revised and strengthened term logic, one fit to challenge the hegemony of predicate logic. The aim was to devise a formal logic that could better serve as the logic of natural language.In recent years a new group of logicians have taken this version of term logic into many new directions. This book presents here for the first time some of the best examples of their work with new essays by philosophers, logicians, mathematicians, computational theorists, and historians of logic. The topics addressed include relative terms, logical copulation, Aristotelian diagrams, modality, truth, semantics, epistemic term logic, non-classical quantifiers, and more.
Visualizing More Quaternions
Visualizing More Quaternions is a sequel to Dr. Andrew J. Hanson's first book, Visualizing Quaternions, which appeared in 2006. This new volume develops and extends concepts that have attracted the author's attention in the intervening 18 years, providing new insights into existing scholarship, and detailing results from Dr. Hanson's own published and unpublished investigations relating to quaternion applications. Among the topics covered are the introduction of new approaches to depicting quaternions and their properties, applications of quaternion methods to cloud matching, including both orthographic and perspective projection problems, and orientation feature analysis for proteomics and bioinformatics. The quaternion adjugate variables are introduced to embody the nontrivial quaternion topology on the three-sphere and incorporate it into machine learning tasks. Other subjects include quaternion applications to a wide variety of problems in physics, including quantum computing, complexified quaternions in special relativity, and a detailed study of the Kleinian "ADE"discrete groups of the ordinary two-sphere. Quaternion geometry is also incorporated into the isometric embedding of the Eguchi-Hanson gravitational instanton corresponding to the k = 1 Kleinian cyclic group. Visualizing More Quaternions endeavors to explore novel ways of thinking about challenging problems that are relevant to a broad audience involved in a wide variety of scientific disciplines.
Debt Dance
Debt Dance: A Global Journey Through Fiscal Tightropes" takes you on a whirlwind tour of government borrowing around the world. It explores the reasons why countries, from emerging economies to established powers, choose to take on debt. You'll discover how these borrowed funds can be used to invest in infrastructure, social programs, or stimulate economic growth. But this book isn't all about the tango. It also delves into the delicate balancing act - the very real risks of excessive debt. We'll explore concepts like inflation, how debt can crowd out private investment, and the burden placed on future generations. "Debt Dance" uses engaging explanations and global examples to shed light on the complex world of sovereign debt. It's a must-read for anyone curious about how nations manage their finances in an interconnected world.
Foundations and requirements of teacher preparation
At the international level, Angola's results in the Mathematics Olympiads are very poor, and at the national level, in Huambo province, these competitions are not developed with the required systematicity. This is largely due to the existence of theoretical and methodological gaps in the teachers' training process.This book provides the fundamentals and requirements for the preparation of teachers in order to improve their performance in the development of the mathematics Olympiads.
Introduction to the Structure of Groups
One of the major and vital concerns that occupies the central positions in Mathematic is the theory of groups.The origin of group theory can be traced to the ardent desire and attempt to determine solutions to some trending problems.Knowledge of groups now plays indispensable roles in such areas like coding theory, counting and the study of symmetries.It is notable to know that biology, chemistry and physics are mutual areas which have greatly benefited from the study and theory of groups.
A Brief Journey from Euclidean to Smarandachean Geometry
The aim of this book is straightforward: to illustrate the true essence of geometry and justify the necessity for the existence of Smarandache geometry. This goal is accomplished by narrating the history of this mathematical field from its origins, akin to a captivating tale featuring characters fixated on depicting spatial forms throughout millennia. The mathematicians portrayed in this narrative exemplify that talent is not solely an intellectual attribute but also demands audacity for transcendence. The first chapter summarizes the book's content, aiming to captivate the reader. The second chapter covers Euclidean Geometry, while the third chapter explores hyperbolic and elliptical geometries, as well as Taxicab and finite geometries. Chapter 4 delves into Smarandache geometries and NeutroGeometries, presenting known and new models. Lastly, the Appendix provides access to Julia language code utilized for generating three-dimensional figures showcased in the book, with the intention of inspiring adept readers to develop software enabling exploration of these spaces virtually. It is hoped that this narrative will engross readers and leave them eager for more at its conclusion.
Mathematics and problem solving
Problem-solving in early childhood education is both possible and fantastic. This paper aims to provide motivation for educators in the field and others interested in the subject. The approach is based on my experience as an educator in the field of mathematics, which every day results in various learning experiences and arouses interest and the need for research into the teaching of mathematics in early childhood education and the search for effective methodologies.
Mathematical Biology
Rich in applications, this text can be used for a semester-long course in differential equations or mathematical biology or serve as a companion text for a 2-semester sequence beginning with discrete time systems, through a wide array of topics in differential equations, culminating in systems, SIR models, & other applications.
Linear Algebra with Applications to Economics
This textbook is intended for students of Mathematical Economics and is based on my lectures on Linear Algebra delivered at Satbayev University in Almaty, Kazakhstan. The program closely aligns with that of the London School of Economics. The textbook extensively utilizes the concept of Gauss-Jordan elimination. Every subspace of the standard coordinate space possesses a unique Gauss basis. This observation significantly clarifies many aspects of Linear Algebra. The covered topics are outlined in the table of contents.
Big Data Analytics and Knowledge Discovery
This book constitutes the proceedings of the 26th International Conference on Big Data Analytics and Knowledge Discovery, DaWaK 2024, which too place in Naples, Italy, during August 26-28, 2024. The 16 full and 20 short papers included in this book were carefully reviewed and selected from 83 submissions. They were organized in topical sections as follows: Modeling and design; entity matching and similarity; classification; machine learning methods and applications; time series; data repositories;optimization; and data quality and applications.
Decomposing G = ( V, E ) into Planar Graphs
This book is our attempt to answer the question, "Is it possible to decompose any graph G with n vertices, lacking any specific symmetry of the underlying structures?" This book presents a solution to this question by developing iterative techniques in an intuitive, simple, and visual way without losing the essence of the underlying mathematics. We trust that this method of decomposing any graph into known subgraphs will open new directions in graph decomposition. This book will be of interest to researchers in graph theory and discrete mathematics.
Statistical Design and Analysis of Experiments
Statistical Design and Analysis of Experiments embraces a holistic approach by building a solid foundation of the theoretical aspects followed by easily relatable numerical examples. Examples are first worked out manually and explained step-by-step, after which the statistical software Minitab is demonstrated throughout the textbook. This novel approach makes the textbook applicable to any undergraduate or graduate course in design of experiments (DOE) as well as a valuable resource in the hands of any experimenter.After a clear introduction, concepts of design and analysis of experiments are introduced. Utilizing practical examples, hypothesis testing and the concepts of Type-I errors, Type-II errors, and Power are clearly explained. ANOVA assumptions as well as tests of significance and the concept of point and interval estimates are discussed. Other topics include various types of experimental designs like trial and error or factorial designs, Yates algorithm, replication and reflection of designs, the concept of confounding, and design resolution. Manual calculations as well as software are used to fully analyze experimental data and to draw clear and meaningful conclusions. Response surface methodology and central composite design follow to optimize designs. The book concludes with the Taguchi method and its pitfalls, and the use of nonparametric or distribution-free statistics for when the ANOVA assumptions are not met.Highly approachable and filled with practical examples, Statistical Design and Analysis of Experiments will teach students to conduct and analyze practical experiments, and draw meaningful conclusions based on a sound theoretical and statistical foundation. The textbook assumes no prior knowledge of statistics and does not rely on the use of calculus. A complete instructors' guide with PowerPoint slides and solutions to end-of-the-chapter questions is available for teachers who adopt the book.
Fundamentals and Principles of Differential Calculus
Differential calculus is a pivotal concept in mathematics and computer science, focusing on techniques to analyze how variations in input parameters influence mathematical quantities or computational results. This book presents a differential calculus theoretical framework and practical applications, emphasizing its significance across various disciplines. This work delves into the study of derivatives differentials. It provides a formalized approach to quantifying rates of change and conducting sensitivity analysis, underscoring the relevance and utility of differential calculus in diverse fields.
An Introduction to Statistical Learning
An Introduction to Statistical Learning provides an accessible overview of the field of statistical learning, an essential toolset for making sense of the vast and complex data sets that have emerged in fields ranging from biology to finance, marketing, and astrophysics in the past twenty years. This book presents some of the most important modeling and prediction techniques, along with relevant applications. Topics include linear regression, classification, resampling methods, shrinkage approaches, tree-based methods, support vector machines, clustering, deep learning, survival analysis, multiple testing, and more. Color graphics and real-world examples are used to illustrate the methods presented. This book is targeted at statisticians and non-statisticians alike, who wish to use cutting-edge statistical learning techniques to analyze their data. Four of the authors co-wrote An Introduction to Statistical Learning, With Applications in R(ISLR), which has become a mainstay of undergraduate and graduate classrooms worldwide, as well as an important reference book for data scientists. One of the keys to its success was that each chapter contains a tutorial on implementing the analyses and methods presented in the R scientific computing environment. However, in recent years Python has become a popular language for data science, and there has been increasing demand for a Python-based alternative to ISLR. Hence, this book (ISLP) covers the same materials as ISLR but with labs implemented in Python. These labs will be useful both for Python novices, as well as experienced users.
Games, Decisions, and Markets
This book critically discusses the historical backgrounds and new developments of the theories of games, decisions, and markets, with many possible applications to social and economic problems. Consisting of three connected parts, the book sheds new light on the role of merchants in the market economy under conditions of risk and uncertainty. Part I begins with the question of why and how John von Neumann and Oskar Morgenstern did joint work in game theory, namely, the theoretical study of strategic interactions among several decision makers. The duel between Sherlock Holmes and Professor Moriarty in Conan Doyle's famous detective story is recalled as a great inducement to Neumann and Morgenstern to invent zero-sum, two-person games. More general non-zero-sum games and associated Nash solutions are then discussed in relation to the generation-gap problem between a young couple and an elderly couple. Part II explores a set of very fundamental problems of individual decision making. Thetwo famous axioms of revealed preference ― Samuelson's weak axiom and Houthakker's axiom ― are skillfully connected and empirically reevaluated by the introduction of certain regularity conditions. The revealed preference approach is then extended from the original commodity space to the dual price space. Such dual treatment in microeconomics is further applied to the theory of cost and production, with the decomposition of the total factor price effect into the substitution and scale effects. Part III turns the reader's attention to the interdependence of several markets. The almost forgotten Hicks-Morishima approach is newly revived with graphical illustrations of traded goods. The well-known Jones-Kemp approach to international trade is boldly expanded into the world of risk and uncertainty. Some striking results in comparative static analysis are derived, with favorable implications for the real world.
The mathematical knowledge of miners in the Matup獺 region
This paper describes an investigation based on Ethnomathematics. This approach, based on its remarkable and comprehensive approach, seeks to demonstrate the ways in which a more productive and lasting teaching practice can be implemented. The aim is to reveal the mathematical knowledge preserved by the miners who live on the outskirts of the municipality of Matup獺-MT, particularly those who did not attend school until the end of secondary school.
Studies on Some Aspects of Difference Sequence Spaces
In the book we have introduced various new sequence spaces in different chapters which generalize many known spaces introduced by several mathematicians. First chapter of this book is the introduction, where as Chapter-II to VI provide certain new classes of difference sequence spaces via Orlicz function. The last chapter is devoted to calculate the spectral sub-divisions of forward difference operator of order "r".
An Introduction to Analysis
This widely popular textbook provides a mathematically rigorous introduction to analysis of real­valued functions of one variable. This intuitive, student-friendly text is written in a manner that will help to ease the transition from primarily computational to primarily theoretical maths.
2021-2022 High School Contest Materials
This book contains one year of mathleague.org high school tests and answer keys: 7 qualifying-level test sets, one state-level test set, and one national-level test set. Each test set contains a Sprint, Target, Team, and Relay test. Three of the test sets also contain a Power Question.
Mathematical modelling Use of public transparency
Teaching maths isn't just about asking students to solve complicated problems, it's about giving them the thoughts, methods and logical reasoning, as well as providing them with the ability to deal with the exact science, giving some the opportunity to choose to follow this marvellous universal path. This book, which is innovative in its teaching ideas due to the encouragement of new technologies, recalls the history of maths teaching and enables the reader to understand why it is necessary to move forward with the use of the most up-to-date resources. It shows the step-by-step process of setting up games or working with mathematical modelling and provides examples that will make it easier for the teacher to understand what is proposed and then work not just with small inspectors, but with curious people with unlimited interests. Learners, who have already been synchronised for a long time, will certainly have the intention of continuing the human legacy on planet Earth. The use of Transparency made available by public bodies during the Modelling games brings the lessons into the reality where the future citizen must act wisely and confidently in the proper understanding of Mathematics. It makes the lesson fun and interesting, and helps solve problems.
Incidence of Technology as a Pedagogical Tool
Technologies have revolutionized education, transforming the way we learn and teach, allowing us to explore their impact on the different levels of curricular concretion, at the macro curricular level: the general objectives, the competencies to be developed and the evaluation criteria are established at a global level, by integrating technologies the teaching strategies are enhanced and fostering the acquisition of digital competencies necessary in today's society; at the meso-curricular level, the specific contents, teaching, learning and evaluation strategies for each particular area or subject are detailed, having as resources the educational platforms such as videos, animations and presentations enrich the educational content and facilitate the understanding of the concept; at the micro-curricular level, the daily activities are planned, defining the didactic resources to be used, the evaluation criteria are established at the level of the didactic units, the technology will improve the interaction in the classroom and personalize the learning process.
Changing methodologies for better maths learning
This research aims to analyse the potential of the connection between Mathematical Modelling and constructivism and its contribution as a methodology in pedagogical practices in the classroom in the teaching-learning process in General Secondary Education (1st Cycle) at Matola Secondary School. This study came about as a result of the realisation that the pedagogical practices in place in the majority of schools do not respond to current social demands, as students are limited to receiving the knowledge transmitted by the teacher without criticising it, which compromises the quality of education and their skills. In view of this, the use of mathematical modelling combined with the constructivist approach contributes to an effective teaching practice, making students active, reflective, participative and capable of producing their own knowledge.
Difficulties in understanding and using rational numbers
This work is concerned with the development of science and technology. It aims to investigate how we can contribute to minimizing the countless situations that interfere with the development of fractional activities in EJA - Youth and Adult Education, and to research the development of strategies for working with tools that can act by enabling and making EJAI students feel more comfortable with rational numbers.
Low Biological Energies
As a complement to the four volumes of the naturalist suite, this essay on low biological energies was needed to explore the transitions between quantum mechanics and statistical physics at work in the integration-level units of the living - proteins, the cell, and the animal. From questioning to questioning the coordination of cellular activity, marine historian and naturalist Claude ROUQUETTE embarks on a navigation at sight, to plumb the depths of low energies in order to take stock of the complex processes in biological evolution, intimately associated with the transformations of civilization.
Image Analysis for Vision-Based Skimming
Infestation with invasive aquatic weeds is a major problem being faced while maintaining inland water bodies. Cleaning the surface pollution ideally requires a fully autonomous trash skimmer with capabilities for detecting the presence and finding the physical location of nearby free- floating weed clusters, collection of weed clusters using cutting of matted weeds, if required, moving the skimmer close to the cluster, collecting the cluster, and moving the collected weeds to the bank. Vision enabled trash skimmer consists of a trash skimmer connected to a vision sensor with capability to capture individual video frames and analyze them to extract desired information. Under these conditions, providing visual information of the surroundings to the trash skimmer will make its operations more convenient, accurate and improve its overall performance. This book focuses on improving the performance of the image processing steps namely horizon line detection techniques for segmenting water regions, object detection algorithm for segmenting floating objects on the water surface, color based edge detection algorithm to estimate green-colored weeds in inland water bodies.
The Challenge of Computing Homotopy Groups
In the grand tapestry of mathematics, topology stands out for its unique approach to geometric shapes. It doesn't care about size or angles, but rather how spaces can be continuously deformed into one another, like stretching a clay model without tearing or gluing separate pieces. This seemingly abstract concept holds immense power, unlocking hidden properties of shapes and revealing a universe beyond our everyday perception of space. One of the central ideas in topology is the notion of a homotopy group. Imagine a loop drawn on a surface, like a circle on a sphere or a square on a plane. Homotopy groups classify these loops based on how they can be continuously deformed into one another without breaking the loop or letting it touch the edge of the surface. Intuitively, a loop that can be shrunk to a point without leaving the surface represents a "trivial" element in the group. More intricate loops that cannot be shrunk but can be continuously deformed into each other belong to the same class within the group.
Economic analysis on a small rural property
Rural properties, regardless of size, need strategies for decision-making. Given this context, this study maps and evaluates three sources of resources on a particular rural property, with the aim of describing business management on small rural properties, emphasizing the need for an ideal evaluation of the viability of economic activities, as a strategic management tool bringing data, statements and results achieved, in order to bring a better perception of the agricultural segment to rural properties and bringing data analyzed through mathematical models that can maximize the profits of the property under study. As such, through this study it can be identified that under the current conditions, dairy production is unviable, compared to the other two activities on the property, providing an optimal model for maximizing profit, which would be the joint production of corn and soybeans, thus maximizing profit.
Games, Gambling, and Probability
The goal for this textbook is to complement the inquiry-based learning movement. According to the author, concepts and ideas will stick with the reader more when they are motivated in an interesting way. Topics are presented mathematically as questions about the games themselves are posed.
Teacher Noticing of Pre-Service and In-Service Secondary Mathematics Teachers
In light of increasing demands on teachers and the need to develop teaching-related competences, this book examines the situation-specific skill of teacher noticing in pre-service and in-service secondary mathematics teachers. A video-based test instrument is used to measure teachers' noticing skills in perception, interpretation, and decision-making from both general and mathematics pedagogical perspectives. The aim is to understand the structure and characteristics of teacher noticing across different groups, as well as the influences of teaching experience and opportunities to learn. Three quantitative studies are conducted: two cross-sectional studies with 457 participants, including master's students, early career teachers, and experienced teachers, and one longitudinal study with 175 master's students. The results support the conceptualization of teacher noticing as comprising three facets. They also reveal positive influences of teaching experience on the development of teacher noticing, with in-service teachers outperforming master's students. However, experienced teachers perform similarly to early career teachers in general and worse in certain areas, suggesting saturation or forgetting effects. The longitudinal study finds that interpretation skills facilitate the development of perception and decision-making, emphasizing the knowledge-based nature of teacher noticing.
Identifiability and Observability in Epidemiological Models
The Mathematical Field
The arithmetic, algebraic and geometric applications can be seen by human beings in:
The Mathematical Field
The arithmetic, algebraic and geometric applications can be seen by human beings in:
AP Precalculus
AP Precalculus: Student Edition is a collection of lessons and activities for every topic in the AP Precalculus course that will be assessed on the AP exam. Each lesson or activity comes with a homework assignment with questions similar to those that will appear on the AP exam. A corresponding teachers' guide and solutions manual, AP Precalculus: The Teacher's Compendium, is available separately.
An Introduction to Stochastic Integration and It繫 Calculus
This book delves into the comprehensive construction of the It繫 theory concerning stochastic integration and its pivotal role, particularly within the framework of stochastic differential equations. The book meticulously examines the distinctive properties of this integral, along with their respective extensions of the It繫 formula, elucidating their significance in various theoretical and practical contexts. Furthermore, the integration theories are seamlessly integrated into the realm of stochastic differential equations, paving the way for examining complex phenomena such as epidemic models, and ecological models. In this context, the book proposes some original theorems to address pertinent issues about its implications within the framework of stochastic differential equations. Through rigorous construction analysis, this book contributes to the advancement of stochastic calculus theory, offering insights into its application in dynamical population modeling.
Statistics Today
This book offers a broad selection of statistical applications to everyday situations, illustrating how exciting and diverse statistical analysis can be. It covers a wide variety of topics, including offering hearing-impaired people the option to enjoy music, extracting meaningful quantitative data from texts, and modeling flood disasters to help get a better grip on them. Most of the examples are not typically found in textbooks but directly relate to real-life problems encountered by the "average person", including topics relevant for sustainable development.Technical jargon and formalism have been avoided as much as possible, and a detailed statistical background is not assumed of the reader, making the book accessible to anyone interested in current research in statistical applications. Providing an unobscured look at a thoroughly fascinating science, it will help students to develop enthusiasm for statistical issues and methods, and may even inspire ideas for their own projects.
Handbook of the Tutte Polynomial and Related Topics
This is the first handbook published on the Tutte Polynomial. It consists of thirty-four chapters, written by experts in the field, that collectively offer a concise overview of the polynomial's many properties and applications. Each chapter covers a different aspect of the Tutte polynomial.
Guaranteed Computational Methods for Self-Adjoint Differential Eigenvalue Problems
This monograph presents a study of newly developed guaranteed computational methodologies for eigenvalue problems of self-adjoint differential operators. It focuses on deriving explicit lower and upper bounds for eigenvalues, as well as explicit estimations for eigenfunction approximations. Such explicit error estimations rely on the finite element method (FEM) along with a new theory of explicit quantitative error estimation, diverging from traditional studies that primarily focus on qualitative results. To achieve quantitative error estimation, the monograph begins with an extensive analysis of the hypercircle method, that is, the Prager-Synge theorem. It introduces a novel a priori error estimation technique based on the hypercircle method. This facilitates the explicit estimation of Galerkin projection errors for equations such as Poisson's and Stokes', which are crucial for obtaining lower eigenvalue bounds via conforming FEMs. A thorough exploration of the fundamental theory of projection-based explicit lower eigenvalue bounds under a general setting of eigenvalue problems is also offered. This theory is extensively detailed when applied to model eigenvalue problems associated with the Laplace, biharmonic, Stokes, and Steklov differential operators, which are solved by either conforming or non-conforming FEMs. Moreover, there is a detailed discussion on the Lehmann-Goerisch theorem for the purpose of high-precision eigenvalue bounds, showing its relationship with previously established theorems, such as Lehmann-Maehly's method and Kato's bound. The implementation details of this theorem with FEMs, a topic rarely covered in existing literature, are also clarified. Lastly, the monograph introduces three new algorithms to estimate eigenfunction approximation errors, revealing the potency of classical theorems. Algorithm I extends Birkhoff's result that works for simple eigenvalues to handle clustered eigenvalues, while Algorithm II generalizes the Davis-Kahan theorem, initially designed for strongly formulated eigenvalue problems, to address weakly formulated eigenvalue problems. Algorithm III utilizes the explicit Galerkin projection error estimation to efficiently handle Galerkin projection-based approximations.
