The mathematical modelling of free and moving boundary problems are an important topic in engineering, industry, technology and theoretical sciences. These models allow us to make calculations involved in phase change transitions of materials due to heat transfer. Boundary layer applications are widespread in research and industry. Boundary Element Methods for Heat Transfer with Phase Change Problems: Theory and Application equips the reader with information about heat transfer problems occurring during phase changes. The book covers several boundary element methods, including methods for phase changes, fixed and moving domains and new approaches. The contents are rounded off with chapters on numerical results and industrial applications. Key features: - Simple, didactic presentation of boundary layer problems for heat transfer problems - Covers a wide range of boundary element methods - Includes methods for fixed and moving domains - Explains industrial applications of the methods - Includes solutions to numerical problems The book serves as a textbook for students of advanced mathematics and engineering. It is also a handbook for researchers working on numerical analysis, who require a focused volume on boundary element methods for heat transfer applications.

The theory of entire and meromorphic functions is a very important area of complex analysis. This monograph aims to expand the discussion about some growth properties of integer translated composite entire and meromorphic functions on the basis of their (p,q,t)L -order and (p,q,t)L -type. This book presents six chapters. Chapter 1 introduces the reader to the preliminary definitions and notations. Chapter 2 and Chapter 3 discuss some results related to (p; q; t) L-th order and (p; q; t)L-th lower order of composite entire and meromorphic functions on the basis of their integer translation. Chapter 4 establishes some relations of integer translated composite entire and meromorphic functions based on their (p; q; t) L-th type and (p; q; t) L-th weak type. Chapter 5 deals with some results about (p; q; t) L-th order and (p; q; t) L-th type of composite entire and meromorphic functions on the basis of their integer translation. Chapter 6 focuses on some results about (p; q; t) L-th order and (p; q; t) L-th type of composite entire and meromorphic functions on the basis of their integer translation. This monograph will be very helpful for postgraduates, researchers, and faculty members interested in value distribution theorems in complex mathematical analysis.

This textbook is a primer for students on statistics. It covers basic statistical operations, an introduction to probability, distributions and regression. The book is divided into a series of 10 chapters covering a basic introduction to common topics for beginners. The goal of the book is to provide a sufficient understanding of how to organize and summarize datasets through descriptive and inferential statistics for good decision-making. A chapter on ethics also informs readers about best practices for using statistics in research and analysis. Topics covered: 1. Introduction to Statistics 2. Summarizing and Graphing 3. Basic Concepts of Probability 4. Discrete Random Variables 5. Continuous Random Variables 6. Sampling Distributions 7. Estimation 8. Hypothesis Testing 9. Correlation and Regression 10. Ethics

Vector calculus is an essential mathematical tool for performing mathematical analysis of physical and natural phenomena. It is employed in advanced applications in the field of engineering and computer simulations. <p></p> This textbook covers the fundamental requirements of vector calculus in curricula for college students in mathematics and engineering programs. Chapters start from the basics of vector algebra, real valued functions, different forms of integrals, geometric algebra and the various theorems relevant to vector calculus and differential forms. <p></p> Readers will find a concise and clear study of vector calculus, along with several examples, exercises, and a case study in each chapter. The solutions to the exercises are also included at the end of the book. <p></p> This is an ideal book for students with a basic background in mathematics who wish to learn about advanced calculus as part of their college curriculum and equip themselves with the knowledge to apply theoretical concepts in practical situations.

High air pollution levels pose a significant threat to plants, animals and human beings. Efforts by researchers are directed towards keeping air pollution levels below well defined ‘critical‘ levels in order to maintain a sustainable atmosphere and environmental system. The application of advanced mathematical models is important for researchers to achieve this goal as efficiently as possible. Mathematical models can be used to predict answers to many important questions about the environment. This application comes with several complex theoretical and practical obstacles which need to be resolved. A successfully applicable mathematical model needs to enable researchers to • Mathematically describe all important physical and chemical processes. • Apply fast and sufficiently accurate numerical methods. • Ensure that the model runs efficiently on modern high speed computers. • Use high quality input data, both meteorological data and emission inventories, in the runs. • Verify the model results by comparing them with reliable measurements taken in different parts of the spatial domain of the model. • Carry out long series of sensitivity experiments to check the response of the model to changes of different key parameters. • Visualize and animate the output results in order to make them easily understandable even to non-specialists. This monograph thoroughly describes mathematical methods useful for various situations in environmental modeling - including finite difference methods, splitting methods, parallel computation, etc. - and provides a framework for resolving problems posed in relation to the points listed above. Chapters are written by well-known specialists making this book a handy reference for researchers, university teachers and students working and studying in the areas of air pollution, meteorology, applied mathematics and computer science.

Time series analysis is applicable in a variety of disciplines, such as business administration, economics, public finance, engineering, statistics, econometrics, mathematics and actuarial sciences. Forecasting the future assists in critical organizational planning activities. Time series analysis is employed by many different organizations such as hospitals, universities, commercial enterprises or government organizations in order to forecast future scenarios. Therefore, many time series forecasting methods have been proposed and improved in statistical literature. Linear models such as Box-Jenkins methods were earlier used in many situations. Then, to overcome the restrictions of these linear models and to account for certain nonlinear patterns observed in real problems, some nonlinear models are also presented in literature. However, since these nonlinear models were developed for specific nonlinear patterns, they are not suitable for modeling other types of nonlinearity in time series. In recent years, efficient and advanced techniques such as artificial neural networks, fuzzy time series and some hybrid models have been used to forecast any kind of real life time series analyses. Both theoretical and empirical findings in academic literature show that these approaches give comparatively reliable forecasts than those obtained from conventional forecasting methods. In addition, conventional models require some assumptions such as linearity and normal distribution or cannot be utilized efficiently for some real time series such as temperature and share prices of stockholders since these kind of series contain some uncertainty. However, when advanced methods such as neural networks and fuzzy time series are used to forecast time series, there is no need to satisfy any assumption and the time series containing uncertainty can be forecasted efficiently. This e-book contains recent effective applications and descriptions of these advanced forecasting methods. Readers will learn how these methods work and how these approaches can be used to forecast real life time series. In addition, the hybrid forecasting model approach, which combines different methods to obtain better forecast results, is also explained. Readers can also find the applications of hybrid forecasting models in this e-book. This e-book also enables skilled statisticians to create a new hybrid forecasting model suitable for their own objectives. Data presented in this e-book is problem based and is taken from real life situations. This e-book is a valuable resource for students, statisticians and working professionals interested in advanced time series analysis.

This volume is a valuable source of recent knowledge about advanced time series forecasting techniques such as artificial neural networks, fuzzy time series, or hybrid approaches. New forecasting frameworks are discussed and their application is demonstrated. The second volume of the series includes applications of some powerful forecasting approaches with a focus on fuzzy time series methods. Chapters integrate these methods with concepts such as neural networks, high order multivariate systems, deterministic trends, distance measurement and much more. The chapters are contributed by eminent scholars and serve to motivate and accelerate future progress while introducing new branches of time series forecasting. This book is a valuable resource for MSc and PhD students, academic personnel and researchers seeking updated and critically important information on the concepts of advanced time series forecasting and its applications.

This book brings together eleven topics on different aspects of fractional calculus in a single volume. It provides readers the basic knowledge of fractional calculus and introduces advanced topics and applications. The information in the book is presented in four parts: 1. Fractional Diffusion Equations: (i) solutions of fractional diffusion equations using wavelet methods, (ii) the maximum principle for time fractional diffusion equations, (iii) nonlinear sub-diffusion equations. 2. Mathematical Analysis: (i) shifted Jacobi polynomials for solving and identifying coupled fractional delay differential equations, (ii) the monotone iteration principle in the theory of Hadamard fractional delay differential equations, (iii) dynamics of fractional order modified Bhalekar-Gejji System, (iv) Grunwald-Letnikov derivatives. 3. Computational Techniques: GPU computing of special mathematical functions used in fractional calculus. 4. Reviews: (i) the popular iterative method NIM, (ii) fractional derivative with non-singular kernels, (iii) some open problems in fractional order nonlinear system This is a useful reference for researchers and graduate level mathematics students seeking knowledge about of fractional calculus and applied mathematics.

The knowledge of quantitative turbulence mechanics relies heavily upon the definition of the concept of a vortex in mathematical terms. This reference work introduces the reader to Liutex, which is an accepted, accurate and mathematical definition of a vortex. The core of this book is a compilation of several papers on the subject. presented in the 13th World Congress of Computational Mechanics (WCCM2018), Symposium 704, Mathematics and Computations for Multiscale Structures of Turbulent and Other Complex Flows, New York, United States on July 27, 2018. This compilation also includes other research papers which explain the work done on the vortex definition, vortex identification and turbulence structure from different insight angles including mathematics, computational physics and experiments. The thirteen chapters in this volume will be informative to scientists and engineers who are interested in advanced theories about fluid dynamics, vortex science and turbulence research.

This book explains uncertainty analysis for finite elements and general nonlinear problems. It starts with the fundamentals of the topic and progresses to complex methods through 9 chapters. Each chapter focuses on a specific, relevant topic and provides information in a structured reading format for advanced learners. The author explains different models relevant to the topic where applicable, in an effort to cover the diverse aspects of mathematical analysis. Topics covered in the book include: - Nonlinear stochastic finite element methods - Reliability calculations - Static analysis of interval finite element - Linear and nonlinear vibration analysis - Stochastic, random, fuzzy and mixed fields - Mixed finite element analysis Uncertainty Analysis in Finite Elements Models is an ideal reference for advanced courses in mathematical analysis and engineering that require students to understand the basics of uncertainty analysis and basic reliability calculations.