Part of New Mathematical Monographs
Not yet published - available from March 2025f
ormat: Hardback
isbn: 9781108493246
Abstract polytopes are partially ordered sets that satisfy some key aspects of the face lattices of convex polytopes. They are chiral if they have maximal symmetry by combinatorial rotations, but none by combinatorial reflections. Aimed at graduate students and researchers in combinatorics, group theory or Euclidean geometry, this text gives a self-contained introduction to abstract polytopes and specialises in chiral abstract polytopes. The first three chapters are introductory and mostly contain basic concepts and results. The fourth chapter talks about ways to obtain chiral abstract polytopes from other abstract polytopes, while the fifth discusses families of chiral polytopes grouped by common properties such as their rank, their small size or their geometric origin. Finally, the last chapter relates chiral polytopes with geometric objects in Euclidean spaces. This material is complemented by a number of examples, exercises and figures, and a list of 75 open problems to inspire further research.
Contains numerous examples, figures and exercises to help readers develop a deeper understanding of the concepts
Does not assume advanced knowledge from other areas of mathematics, to remain accessible to beginning graduate and advanced undergraduate students
Lists open problems to inspire readers in their own research
1. Introduction
2. Abstract regular and chiral polytopes
3. Groups related to chiral polytopes
4. Polytopes constructed from other polytopes
5. Families of chiral polytopes
6. Skeletal polytopes
A. A few treats on Euclidean geometry
B. A few words about numbers
C. Open problems
References
Index.
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Hardback
ISBN 9781032845159
130 Pages
Published November 1, 2024 by
This book introduces path-breaking applications of concepts from mathematical topology to music-theory topics including harmony, chord progressions, rhythm, and music classification. Contributions address topics of voice leading, Tonnetze (maps of notes and chords), and automatic music classification.
Focusing on some geometrical and topological aspects of the representation and formalisation of musical structures and processes, the book covers topological features of voice-leading geometries in the most recent advances in this mathematical approach to representing how chords are connected through the motion of voices, leading to analytically useful simplified models of high-dimensional spaces; It generalizes the idea of a Tonnetz, a geometrical map of tones or chords, and shows how topological aspects of these maps can correspond to many concepts from music theory. The resulting framework embeds the chord maps of neo-Riemannian theory in continuous spaces that relate chords of different sizes and includes extensions of this approach to rhythm theory. It further introduces an application of topology to automatic music classification, drawing upon both static topological representations and time-series evolution, showing how static and dynamic features of music interact as features of musical style.
This volume will be a key resource for academics, researchers, and advanced students of music, music analyses, music composition, mathematical music theory, computational musicology, and music informatics. It was originally published as a special issue of the Journal of Mathematics and Music.
Introduction
Moreno Andreatta, Emmanuel Amiot, Jason Yust
1. Why Topology?
Dmitri Tymoczko
2. Generalized Tonnetze and Zeitnetze, and the Topology of Music Concepts
Jason Yust
3. Homological Persistence in Time Series: An Application to Music Classification
Mattia G. Bergomi and Adriano Barate
Hardback
ISBN 9781032555973
226 Pages
Published November 19, 2024
A First Course on Orthogonal Polynomials: Classical Orthogonal Polynomials and Related Topics provides an introduction to orthogonal polynomials and special functions aimed at graduate students studying these topics for the first time. A large part of its content is essentially inspired by the works of Pascal Maroni on the so-called algebraic theory of orthogonal polynomials, which distinguishes it from other contributions in the field.
Suitable for a graduate course in orthogonal polynomials
Can be used for a short course on the algebraic theory of orthogonal polynomials and its applicability to the study of the “old” classical orthogonal polynomials
Includes numerous exercises for each topic
Real and complex analysis are the only prerequisites
1. Foundations of the algebraic theory. 2. Orthogonal polynomial sequences. 3. Zeros and Gauss-Jacobi mechanical quadrature. 4. The spectral theorem. 5. The Markov theorem. 6. Orthogonal polynomials and dual basis. 7. Functional differential equation. 8. Classical orthogonal polynomials: General properties. 9. Functional equation on lattices. 10. Classical orthogonal polynomials: The positive definite case. 11. Hypergeometric series. A. Locally Convex Spaces.
Hardback
ISBN 9781032663128
332 Pages 3 B/W Illustrations
Published November 14, 2024
Fixed point theory is a powerful tool in nonlinear analysis, with applications in fractional differential equations and other areas. The most prominent application/conclusion of this theory is the Banach contraction principal. The notion of invisible graphs, introduced here for the first time, will find applications in different areas of science.
The book examines the classical techniques of this theory with a critical approach, along with the emergence of various generalizations in its evolution. Using the latest theories of the philosophy of science, the author aims to provide a philosophical explanation for the gaps in the fixed point theory and introduce the reader to profound mathematical-philosophical challenges.
Preface. Introduction. Orders, cones and graphs. Metric structures. Some modern fixed point results. Fixed point results for set-valued mappings. Some types of α-ψ-contractive set-valued mappings. Quasi-contractions and T-stability. Some false results on rate of convergence. Some false generalizations. References.
Hardback
ISBN 9781032862446
394 Pages 7 B/W Illustrations
Published December 30, 2024
Mathematical Analysis: Theory and Applications provides an overview of the most up-to-date developments in the field, presenting original contributions and surveys from a spectrum of respected academics. Readers will discover numerous valuable tools and techniques to enhance their understanding of recent advancements in mathematical analysis and its applications. Each chapter highlights new research directions, making this book suitable for graduate students, faculty, and researchers with an active interest in the development of mathematical analysis and its practical implementation. Minimal prerequisites in analysis, topology, and functional analysis are required for readers to fully benefit from the content.
Showcases the latest advancements in these areas by featuring contributions from distinguished scientists and mathematicians from around the world
Suitable as a reference for postgraduate students and researchers
Explores future research directions
1. Fixed Point Theory: Recent developments, Challenges and Open Problems
Pradip Debnath
2. Several recent episodes on the metric completeness
Sehie Park
3. Fixed point theorems in p-normed spaces
George Xianzhi Yuan and Jian-Zhong Xiao
4. New versions of Kannan type map
Nihal Tas
5. Some applications of a Kittaneh inequality to operator-valued integrals on Hilbert Spaces
Sever Dragomir
6. Frozen derivative iterative methods of high order for equations
Ioannis K. Argyros and Gagan Deep
7. Application of some classes of Mittag-Leffler functions in solving conformal fractional differential equations
Arsalan Hojat Ansari, Snjezana Maksimovic, Hossam A. Nabwey, and Zoran D. Mitrovic
8. The non-population conserving SIR model on time scales
Zahra Belarbi, Benaoumeur Bayour, and Delfim F. M. Torres
9. Stability criteria of nonlinear generalized proportional fractional delayed systems
Hanaa Zitane and Delfim F. M. Torres
10. On the Hamburger-Oberhettinger-Soni modular relations
Kalyan Chakraborty, Shigeru Kanemitsu, and L. -W. Yu
11. Extended and efficient secant-type methods based on generalized Schmidt-Schwetlick conditions
Ioannis K. Argyros, Jinny Ann John, and Jayakumar Jayaraman
12. Summation of Schlomilch-type series
Slobodan B. Trickovic and Miomir S. Stankovic
13. Cross diffusion driven instability and non-linear analysis in a spatio-temporal oncolytic therapeutic model
Fatiha Najm, Radouane Yafia, and M. A. Aziz Alaoui
14. From metric spaces to O-metric spaces: Generalizing the metrical triangle inequality
Hallowed O. Olaoluwa, Aminat O. Ige, and Johnson O. Olaleru
15. Stability analysis of a diffusive SVIR epidemic model with distributed delay, imperfect vaccine and general incidence rate
Achraf Zinihi, Mostafa Tahiri, Moulay Rchid Sidi Ammi
16. Gauss-Newton methods for convex composite optimization under generalized continuity conditions
Ioannis K. Argyros, Santosh George, and Michael Argyros
Hardback
ISBN 9781032642451
314 Pages 11 Color & 6 B/W Illustrations
Published December 30, 2024
Description
This book covers contemporary topics in mathematical analysis and its applications and relevance in other areas of research. It provides a better understanding of methods, problems, and applications in mathematical analysis. It also covers applications and uses of operator theory, approximation theory, optimization, variable exponent analysis, inequalities, special functions, functional equations, statistical convergence and some function spaces, and presents various associated problems and ways to solve such problems. The book provides readers a better understanding of discussed research problems by presenting related developments in reasonable details. It strives to bring scientists, researchers and scholars together on a common platform.
Preface
1. Approximation Results for Stochastic Processes via Statistical Convergence Based on a Power Series
Emre Ta?
2. Fractional Korovkin-type Results by P-statistical Convergence
Tu?ba Yurdakadim
3. Two Approaches for Evaluating the Period Function of Some Hamiltonian Systems
Daniele Ritelli and Giulia Spaletta
4. Continuous Characterizations of Weighted Besov and Triebel-Lizorkin-Type Spaces
Ahmed Loulit
5. Variable Exponent Vanishing Morrey Type Spaces on Unbounded Domains
Ferit Gurbuz
6. Boundedness of the Intrinsic Square Function on Herz Spaces with Variable Exponents
Liwei Wang
7. q-Deformed and λ-Parametrized Hyperbolic Tangent Function Relied Complex Valued Trigonometric and Hyperbolic Neural Network High Order Approximations
George A. Anastassiou
8. Nonlinear Exponential Sampling: Approximation Results and Applications
Danilo Costarelli
9. Refinements and Reverses of Some Inequalities for the Normalized Determinants of Sequences of Positive Operators on Hilbert Spaces
Silvestru Sever Dragomir
10. Fuzzy Inference Based Approach of Ant Colony Optimization (ACO) in Fuzzy Transportation Models
M.K. Sharma, Tarun Kumar, Laxmi Rathour and Vishnu Narayan Mishra
Index