This reference explains hybrid-Trefftz finite element method (FEM). Readers are introduced to the basic concepts and general element formulations of the method. This is followed by topics on non-homogeneous parabolic problems, thermal analysis of composites, and heat conduction in nonlinear functionally graded materials. A brief summary of the fundamental solution based-FEM is also presented followed by a discussion on axisymmetric potential problems and the rotordynamic response of tapered composites. The book is rounded by chapters that cover the n-sided polygonal hybrid finite elements and analysis of piezoelectric materials. Key Features - Systematic presentation of 9 topics - Covers FEMs in two sections: 1) hybrid-Trefftz method and 2) fundamental FEM solutions - Bibliographic references - Includes solutions to problems in the numerical analysis of different material types - Includes solutions to some problems encountered in civil engineering (seepage, heat transfer, etc). This reference is suitable for scholars involved in advanced courses in mathematics and engineering (civil engineering/materials engineering). Professionals involved in developing analytical tools for materials and construction testing can also benefit from the methods presented in the book.

Mathematical transformations have applications in many everyday artistic (computer graphics and design), industrial (manufacturing) and scientific (informatics) processes. Transformations: A Mathematical Approach covers both the mathematical basics of transformations and technical applications. Readers will find information on the mathematical operators for linear, nonlinear and affine transformations. Key Features -introduces readers to affine transformations, their properties and definitions -explains different linear and nonlinear transformations -covers the application of transformations in acoustics, actuary, bioinformatics, calculus, cybernetics, epidemiology, genetics, optics, physics, probability and vector analysis -includes carefully selected examples for easy understanding The combination of an easy-to understand text with information on a broad range of basic and applied topics related to transformations makes this textbook a handy resource for students of mathematics and allied disciplines, at all levels.

This is an ideal textbook for researchers interested in sampling methods, survey methodologists in government organizations, academicians, and graduate students in statistics, mathematics and biostatistics. This textbook makes advanced topics easy to grasp for the readers. Many theoretical discussions about the latest estimators in literature are incorporated into almost all the chapters. This feature helps the academicians acquire necessary skills to follow up recent studies on their own. More than just an introductory text, the reader, who has mastered the contents of this book, should attain a level so as to be able to make a major contribution to the technical and research literature of sampling theory.

In recent years, special functions have been developed and applied in a variety of fields, such as combinatory, astronomy, applied mathematics, physics, and engineering due to their remarkable properties. This volume expands our understanding of special functions by highlighting recent trends in numerical analysis. are demonstrated by 15 chapters. Many chapters highlight the importance of fundamental results and techniques of the theory of complex analysis for partial differential equations Contributions emphasize articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. This volume is a timely update for mathematicians and researchers interested in advanced numerical methods and computational techniques used to solve complex problems List of Chapters 1. Modified Adaptive Synchronization and Anti Synchronization method for Fractional order chaotic systems with uncertain parameters 2. Improved generalized differential transform method for a class of linear non homogeneous ordinary fractional differential equation 3. Incomplete K2-Function 4. Some Results On Incomplete Hypergeometric Functions 5. Transcendental Bernstein Series: Interpolation and Approximation 6. Some Sufficient Conditions For Uniform Convexity Of Normalized 1F2 Function 7. From Abel continuity theorem to Paley-Wiener theorem 8. A New Class of Truncated Exponential-Gould-Hopper basedGenocchi Polynomials 9. Computational preconditioned Gauss-Seidel via half-sweep approximation to Caputo's time fractional differential equations 10. Krasnoselskii-type Theorems for Monotone Operators in Ordered Banach Algebra with Applications in Fractional Differential Equations and Inclusion 11. General fractional order quadratic functional integral equations: Existence, properties of solutions and some of its Applications 12.Nonlinear set-valued delay functional integral equations of Volterra-Stieltjes type: Existence of solutions, continuous dependence and applications 13.Certain Saigo Fractional Derivatives Of Extended Hypergeometric Functions 14. Some Erdelyi-kober Fractional Integrals Of The Extended Hypergeometric Functions 15. On solutions of Kinetic Model by Sumudu transform

Markov Chain Process: Theory and Cases is designed for students of natural and formal sciences. It explains the fundamentals related to a stochastic process that satisfies the Markov property. It presents 10 structured chapters that provide a comprehensive insight into the complexity of this subject by presenting many examples and case studies that will help readers to deepen their acquired knowledge and relate learned theory to practice. This book is divided into four parts. The first part thoroughly examines the definitions of probability, independent events, mutually (and not mutually) exclusive events, conditional probability, and Bayes' theorem, which are essential elements in Markov's theory. The second part examines the elements of probability vectors, stochastic matrices, regular stochastic matrices, and fixed points. The third part presents multiple cases in various disciplines: Predictive computational science, Urban complex systems, Computational finance, Computational biology, Complex systems theory, and Computational Science in Engineering. The last part introduces learners to Fortran 90 programs and Linux scripts. To make the comprehension of Markov Chain concepts easier, all the examples, exercises, and case studies presented in this book are completely solved and given in a separate section. This book serves as a textbook (either primary or auxiliary) for students required to understand Markov Chains in their courses, and as a reference book for researchers who want to learn about methods that involve Markov Processes.

The Stokes phenomenon refers to the emergence of jump discontinuities in asymptotic expansions at specific rays in the complex plane. This book presents a radical theory for the phenomenon by introducing the concept of regularization. Two methods of regularization, Borel summation and Mellin-Barnes regularization, are used to derive general expressions for the regularized values of asymptotic expansions throughout the complex plane. Though different, both yield identical values, which, where possible, agree with the original functions. Consequently, asymptotics has been elevated to a true discipline yielding precise solutions. All researchers, who seek asymptotic solutions to problems, will find this a most valuable book.

In The Generalized Relative Gol‘dberg Order and Type: Some Remarks on Functions of Complex Variables, the authors have discussed the generalized comparative growth analysis of entire functions of several complex variables at length. The discussion covers the important branch of complex analysis specially the theory of analytic functions of several variables. The book contains eight chapters. Chapter 1 presents introductory aspects of the topic and some preliminary definitions. In the proceeding chapters (2-8), the authors derive some results about the generalized Gol'dberg order (α,β) and generalized Gol'dberg type (α,β) of entire functions of several complex variables which progressively explores different variations of these variables, (upper and lower, functions, inequalities, growth measures). The book culminates in an explanation of the sum and product theorems depending on the generalized relative Gol'dberg order (α,β). This monograph is intended for mathematical researchers and enthusiasts who wish to expand their understanding about complex variables of several functions and complex and related aspects of complex analysis.

The theory of summability has many uses throughout analysis and applied mathematics. Engineers and physicists working with Fourier series or analytic continuation will also find the concepts of summability theory valuable to their research. The concepts of summability have been extended to the sequences of fuzzy numbers and also to the theorems of ergodic theory. This ebook explains various aspects of summability and demonstrates applications in a coherent manner. The content can readily serve as a useful series of lecture notes on the subject. This ebook comprises of 8 chapters starting from classical sequence spaces and covering matrix transformations and fuzzy numbers. An accompanying bibliography with extensive references makes this a valuable source of information for readers interested in summability theory as well as other branches of science.

This book explains different types of subharmonic and harmonic functions. The book brings 12 chapters explaining general and specific types of subharmonic functions (eg. quasinearly subharmonic functions and other separate functions), related partial differential equations, mathematical proofs and extension results. The methods covered in the book also attempt to explain different mathematical analyses such as elliptical equations, domination conditions, weighted boundary behavior. The book serves as a reference work for scholars interested in potential theory and complex analysis.

Applications of Blockchain in Cybersecurity Solutions is a comprehensive guide to blockchain applications in computer security. it presents the concepts and practical techniques that are useful in creating and designing decentralized cybersecurity software through 9 carefully edited chapters. Topics covered in the book include - An introduction to the use of blockchain technology in cybersecurity - Attack surfaces in blockchains - Anti-counterfeit solutions in blockchains - blockchain based access control systems - Multi-chain security deployment over smart contracts - Cybersecurity as a decentralized service The book is an essential primer for computer science students and researchers, and a quick reference for IT professionals on blockchain based cybersecurity.