Format: Hardback, 300 pages, height x width: 235x155 mm, 5 Illustrations, color; Approx. 300 p. 5 illus. in color., 1 Hardback
Pub. Date: 12-Oct-2025
ISBN-13: 9783031995453
This monograph originates from a study of the continued fraction z = [ 1, 2, 3, ...], which we call the Zopf number. Its origins date back to 1929 when Siegel introduced it as a ratio of Bessel functions. Continued fractions is most often styled classically, and much of the content is formulated through Diophantine analysis. However, in this book aspects of the theory of computation can be used interchangeably through matrices and transducers.
We give an introduction to the computational theory of continued fractions, viewed through the lens of matrices and transducers. Then we move to quadratic convergents in terms of the classical rational convergents, which is one of the main topics of the book. With this at hand, the Zopf number and its quadratic convergents are explored through Diophantine analysis. This is followed by the generalized Zopf numbers which can be written compactly in terms of irregular continued fractions, for which many can be shown to have representations by Hurwitz continued fractions. For these Hurwitzian Zopf numbers, we provide an algorithm for converting from irregular to regular continued fractions by using a special type of "interrupted" LR-sequences. Finally, applications to these Hurwitzian Zopf numbers are given, including a refinement of the irrationality measure by iterated logarithms.
Written in an accessible style, the material will be of interest to students and researchers in number theory and approximation theory.
I. A classical introduction to continued fractions and quadratic
convergents.- II. The Zopg constant [ 1,2,3,...] and its relatives.- III.
Matrices and transducers: The computational theory of continued fractions.-
IV. The theory of conversions from irregular to regular Hurwitz continued
fractions.- V. On a refinement of the irrationality measure.- VI. Appendix.
Format: Hardback, 164 pages, height x width: 235x155 mm, 51 Illustrations, color; VIII, 164 p. 51 illus. in color., 1 Hardback
Pub. Date: 01-Oct-2025
ISBN-13: 9783031969928
This book provides an in-depth examination of fractal functions, focusing on their self-similar structures and the relatively simple construction procedures that make them a subject of fascination in mathematics and engineering. By exploring fractal interpolation functions, the book sheds light on naturally occurring phenomena that exhibit irregularity and non-integer dimensions, offering a fresh perspective on these complex mathematical constructs.
The chapters cover a range of topics, including the foundational principles of fractal geometry, the construction of fractal functions through iterated function systems, and the critical role of scaling parameters. Readers will find expert analyses of affine and non-affine fractal functions, as well as discussions on the application of fractional calculus methods such as the Riemann-Liouville and Caputo derivatives. The book also explores the practical applications of fractal interpolation in areas like epidemiology and climate dynamics, demonstrating the relevance of these mathematical concepts to real-world problems.
This volume is an essential resource for researchers and scholars in mathematics, engineering, and related fields. It offers a comprehensive overview of the current research on fractal functions and fractional calculus, providing readers with the tools to understand and apply these concepts in their work. Whether you are an academic seeking to deepen your knowledge or a practitioner looking to apply fractal functions to practical challenges, this book is a valuable addition to your library. It invites you to engage with the latest research and explore the potential of fractal functions in addressing complex scientific and engineering problems.
Fractal Geometry.- Fractal Functions An Overview.- Fractal Interpolation
Vs Classical Interpolation.- Fractal Splines.- Fractal Co efficients.-
Classical Integration on Fractal Functions.- Methods of Fractional Calculus.-
Fractional Derivative Order and Fractal Scalings.- Fractional Integral Order
and Fractal Scalings.- Applications of Fractal Interpolation Functions.
Format: Paperback / softback, 218 pages, height x width: 235x155 mm, X, 218 p., 1 Paperback / softback
Series: Mathematical Marvels: Texts and Monographs in the Spirit of CR Rao
Pub. Date: 24-Sep-2025
ISBN-13: 9789819695478
This book presents a systematic treatment of Henstock–Orlicz (or H-Orlicz) spaces with minimal assumptions on the Young function. H-Orlicz spaces contain non-absolute integrable functions called Henstock–Kurzweil integrable functions. Results from classical functional analysis are presented in detail, and new material is included on classical analysis. Extrapolation is used to prove, for example, the countable additivity of Henstock–Dunford integrable functions on H-Orlicz spaces are included. Relationships of modular convergence and norm convergence of H-Orlicz spaces are discussed. Finally, central geometrical results are provided for H-spaces, including uniformly convexity, reflexivity and the Radon–Nikodym property of the H–Orlicz spaces. Primarily aimed at researchers and PhD students interested in Orlicz spaces or generalized Orlicz spaces, this book can be used as a basis for advanced graduate courses in analysis.
Chapter 1. Basic Ingredients.
Chapter 2. Orlicz spaces.
Chapter 3. Historical Background of Non-absolute Integrals.
Chapter 4. Kluvįnek-Lewis-Henstock Integrals.
Chapter 5. Henstock-Dunford and Henstock-Pettis Integrable Functions.
Chapter 6. Henstock-Orlicz Spaces and Denseness of C.
Chapter 7. Geometrical Properties of Henstock-Orlicz Spaces.
Chapter 8. Weak Henstock-Orlicz Spaces and Inclusion Properties.-
Chapter 9. Countable Additivity of Henstock-Dunford Integrable Function and Orlicz Spaces.
Chapter 10 Modular convergence in H-Orlicz spaces of Banach valued functions.
Format: Hardback, 271 pages, height x width: 235x155 mm, X, 271 p., 1 Hardback
Series: Industrial and Applied Mathematics
Pub. Date: 27-Sep-2025
ISBN-13: 9789819696734
This book contains select chapters on topics related to nonlinear dynamics and functional analysis and their applications in quantum transport, carbon nanotubes, approximation theory, fixed point theory, quantum functional calculus, renewable natural resources, dynamic optimal control model and optimal control analysis. It focuses on bridging the gap between recent trends of interdisciplinary research in nonlinear dynamics and functional analysis. This book helps researchers, scientists and students in obtaining cutting-edge research in these areas and opens the pavement to apply nonlinear dynamics and functional analysis to solve interdisciplinary problems in several areas.
Chapter 1 A Qualitative Study for Nonsmooth Dynamical Systems.
Chapter 2 Nonlinear Dynamics, Chaos and Instability Control in Chemical Reactions.-
Chapter 3 Influence of a Depensatory Growth Function for a Renewable Resource, in an Open Access Fisheries Model.
Chapter 4 HyersUlam Stability Analysis of an Impulsive Fractional Dynamic Equation with Non-local Initial Condition on Time Scales.
Chapter 5 On Stability Analysis of Solutions for a Class ofA Nonlinear Integral Equations of Fractional Order in Banach Algebra.
Chapter 6 Lie Symmetry Analysis of a Mathematical Model for COVID-19.
Chapter 7 On Integral Inequalities of HermiteHadamard Type.-
Chapter 8 An Existence Result for Hadamard Fractional Integral Equations via Fixed Point Theorem.
Chapter 9 LRS Bianchi Type-I Universe with Hybrid Expansion Law and Rényi Holographic Dark Energy.
Chapter 10 Soret and Thermal Radiation Effects on Oscillatory Magnetohydrodynamic Flow of Viscoelastic Fluid in a Porous Channel.
Chapter 11 A Numerical Investigation of Hybrid Ag-Cu/blood MHD Flow in a Stenosed Arterial System under the Influence of Radiation over a Porous Medium.
Chapter 12 Natural Convective Hydrodynamic Radiative Flow of a Chemically Reacting Fluid through Porous Plate.-
Chapter 13 Free Convective MHD Mass Transfer Flow Past an Infinite Vertical Porous Plate with Uniform Heat and Mass Flux Embedded in a Porous Medium.
Format: Hardback, 207 pages, height x width: 235x155 mm, 39 Illustrations, color; 3 Illustrations, black and white; X, 207 p. 42 illus., 39 illus. in color., 1 Hardback
Series: Springer Series in Operations Research and Financial Engineering
Pub. Date: 24-Sep-2025
ISBN-13: 9783031985751
This book explores regime-switching Brownian motion, a class of stochastic processes widely used in fields such as mathematical finance, risk theory, queueing theory, and epidemiological modeling. These processes are studied within the Markovian regime-switching framework, which captures dynamic environments characterized by shifts between different states or "regimes"—for example, economic cycles, seasonal environmental variations, or short-term surges in activity.
The matrix-analytic approach, introduced approximately fifty years ago in the context of classical queueing theory, serves as the foundation for this analysis. This methodology emphasizes the examination of process trajectories over time, drawing insights from the interplay between analytic derivations and their physical or probabilistic interpretations. A central objective of the matrix-analytic framework is to produce solutions that are not only analytically tractable but also amenable to efficient, stable numerical algorithms—facilitating practical implementation using standard computational tools. This enables both quantitative performance evaluation and qualitative system understanding.
Originally developed for telecommunication network modeling, matrix-analytic methods have since found applications across a broad spectrum of disciplines, including risk analysis, branching processes, and epidemiology.
This book is the first to offer a systematic application of matrix-analytic techniques to Markov-modulated Brownian motion, filling a gap in the literature and providing a valuable resource for researchers and practitioners alike.
The intended audience includes specialists in stochastic processes and their applications—such as applied probabilists, actuaries, financial analysts, systems and operations researchers, applied statisticians, and engineers in telecommunications and electrical domains. Readers are expected to have a background in advanced undergraduate calculus, linear algebra, and introductory stochastic processes.
Preface.- Preliminaries.- First Passage Across a Level.- Exit from an
interval.- Expected local time.- Regulated Processes.- Algorithms.-
Conclusion.- References.- Index.
Format: Paperback / softback, 111 pages, height x width: 235x155 mm, 3 Illustrations, color;
36 Illustrations, black and white; X, 111 p. 39 illus., 3 illus. in color., 1 Paperback / softback
Series: SpringerBriefs in Statistics
Pub. Date: 08-Sep-2025
ISBN-13: 9783031997969
This book consolidates knowledge on regression chain graph models, often referred to as regression graph models, with a particular emphasis on their parameterizations and inference for the analysis of categorical data. It presents regression graphs, their interpretation in terms of sequences of multivariate regressions, interpretable parameterizations for categorical data, and inference and model selection within the frequentist and Bayesian approaches. The aim is to reveal the benefits of this family of graphical models for statistical data analysis and to encourage applications of these models as well as further research in the field. Data and R code used in the book are available online. The text is primarily intended for graduate and PhD students in statistics and data science who are familiar with the basics of graphical Markov models and of categorical data analysis, and for motivated researchers in specific applied fields.
Preface.- 1 Regression Graph Models.- 2 Multivariate Logistic Regression
Models.- 3 Maximum Likelihood Inference.- 5 Bayesian Inference.- References.-
Index.
Format: Paperback / softback, 250 pages, height x width: 235x155 mm, Approx. 250 p., 1 Paperback / softback
Series: Springer Undergraduate Mathematics Series
Pub. Date: 30-Sep-2025
ISBN-13: 9783031995422
This book introduces qualitative methods for understanding differential equations, especially when analytical solutions are not possible. Aimed at second-year undergraduate students in mathematics or science, it assumes prior knowledge of calculus, linear algebra, and curve sketching. The book focuses on phase plane methods for second-order differential equations, supported by earlier sections on analytical techniques and phase lines for first-order equations. The later chapters explore bifurcation theory and chaos. Emphasizing application over theory, the book includes diagrams, worked examples, and exercises, with minimal use of formal proofs.
Chapter 1. Introduction.
Chapter 2. Analytical Methods for Differential Equations.
Chapter 3. Qualitative Methods for First-Order Differential Equations.
Chapter 4. Second-Order Linear Systems.
Chapter 5. Second-Order Nonlinear Systems.
Chapter 6. Bifurcations.
Chapter 7. Difference Equations.
Chapter 8. Chaos.
Chapter 9. Solutions to Odd-Numbered Exercises.