Format: Hardback, 141 pages, height x width: 235x155 mm, 8 Illustrations, color; X, 141 p. 8 illus. in color.
Series: Industrial and Applied Mathematics
Pub. Date: 12-Apr-2025
ISBN-13: 9789819624751
This book presents original research on the theory of positive operators, alongside fixed-point theorems and their diverse applications. It introduces various positive operators and explores their approximation properties, including Korovkin-type theorems, Voronovskaja-type results, convergence rate, and other related findings. Additionally, the book addresses the existence of solutions for various differential and integral equations in different Banach spaces by using Darbo-type fixed-point theorems. This book also presents an interplay between positive operators and fixed-point theory. Each chapter is self-contained, addressing a current problem and outlining solutions and potential applications. The chapters provide sufficient background to ensure that new definitions and results can be understood independently.
Chapter 1 Convergence of a Class of SzaszKantorovich Operators based on 2D Appell Polynomials .
Chapter 2 Convergence Results for Nonlinear Generalized Bernstein-type Operators.
Chapter 3 Existence of Solutions for Infinite System of Nonlinear q-fractional Boundary-value Problem via
Generalized Darbos Fixed-point Theorem.
Format: Hardback, 157 pages, height x width: 235x155 mm, 1 Illustrations, black and white; XI, 157 p. 1 illus.,
Series: Infosys Science Foundation Series in Mathematical Sciences
Pub. Date: 17-Apr-2025
ISBN-13: 9789819625987
The book explores and investigates a long-standing mathematical question whether a product of two or more positive integers in an arithmetic progression can be a square or a higher power. It investigates, more broadly, if a product of two or more positive integers in an arithmetic progression can be a square or a higher power. This seemingly simple question encompasses a wealth of mathematical theory that has intrigued mathematicians for centuries. Notably, Fermat stated that four squares cannot be in arithmetic progression. Euler expanded on this by proving that the product of four terms in an arithmetic progression cannot be a square. In 1724, Goldbach demonstrated that the product of three consecutive positive integers is never square, and Oblath extended this result in 1933 to five consecutive positive integers. The book addresses a conjecture of Erds involving the corresponding exponential Diophantine equation and discusses various number theory methods used to approach a partial solution to this conjecture.
This book discusses diverse ideas and techniques developed to tackle this intriguing problem. It begins with a discussion of a 1939 result by Erds and Rigge, who independently proved that the product of two or more consecutive positive integers is never a square. Despite extensive efforts by numerous mathematicians and the application of advanced techniques, Erds' conjecture remains unsolved. This book compiles many methods and results, providing readers with a comprehensive resource to inspire future research and potential solutions. Beyond presenting proofs of significant theorems, the book illustrates the methodologies and their limitations, offering a deep understanding of the complexities involved in this mathematical challenge.
Chapter 1 Preliminaries: A Tool Kit.
Chapter 2 Basic ideas of Erdos.-
Chapter 3 Theorem of Sylvester.
Format: Paperback / softback, 133 pages, height x width: 240x168 mm, 2 Illustrations, color; X, 133 p. 2 illus. in color.,
Series: Frontiers in Mathematics
Pub. Date: 06-May-2025
ISBN-13: 9783031833717
This book presents the new fascinating area of continuous inequalities. It was recently discovered that several of the classical inequalities can be generalized and given in a more general continuous/family form. The book states, proves and discusses a number of classical inequalities in such continuous/family forms. Moreover, since many of the classical inequalities hold also in a refined form, it is shown that such refinements can be proven in the more general continuous/family frame.
Written in a pedagogical and reader-friendly way, the book gives clear explanations and examples on how this technique works. The presented interplay between classical theory of inequalities and these newer continuous/family forms, including some corresponding open questions, will appeal to a broad audience of mathematicians and serve as a source of inspiration for further research.
- 1. Continuous Forms of Classical Inequalities.- 2. Refinements of
Continuous Forms of Inequalities.- 3. Refinements of Inequalities via Strong
Convexity and Superquadracity.- 4. Functionals Associated with Continuous
Forms of Inequalities.- 5. Some Classical Inequalities Involving Banach
Lattice Norms.
Format: Paperback / softback, 293 pages, height x width: 235x155 mm, 55 Illustrations, color;
336 Illustrations, black and white; XI, 293 p. 391 illus., 55 illus. in color.,
Series: Compact Textbooks in Mathematics
Pub. Date: 10-Apr-2025
ISBN-13: 9783031821622
The main objective of the book is to teach how to practically construct periodic tessellations with stars and rosettes using an Interactive Geometry Software (IGS).
Stars and rosettes are among the most characteristic geometric ornamental motifs of Islamic art. They are found on walls, ceilings, doors, and windows in both religious and secular buildings. Tessellations are repetitive patterns of shapes that fit together without gaps or overlaps, and they are periodic when they can be constructed by translations of a shape in two different directions. Periodic tessellations with stars and rosettes are complex and symmetrical compositions with rhythmic repetitions of profound beauty. An IGS allows to create and manipulate geometric constructions, producing accurate drawings. The book only assumes knowledge of basic geometric concepts and is self-contained while also providing all the necessary background information.
Tessellations with Stars and Rosettes is aimed at students and graduates of mathematics, design, architecture, artists, and art historians, as well as anyone who wants to draw tessellations of stars and rosettes using IGS. It is suitable for a trimester or a semester course, and can also be used for self-study.
1. Introduction.- 2. Preliminaries.-
3. Regular Stars, rosettes and tessellations with stars and rosettes.-
4. Design of tessellations with stars and rosettes.
Format: Paperback / softback, 785 pages, height x width: 235x155 mm, 191 Illustrations, color;
71 Illustrations, black and white; XVIII, 785 p. 262 illus., 191 illus. in color.,
Series: Undergraduate Texts in Physics
Pub. Date: 12-Apr-2025
ISBN-13: 9783031813146
This textbook serves as a comprehensive introduction to quantum technology for advanced undergraduate and beginning graduate students in physics and engineering. It provides readers with an in-depth overview of the wide range of quantum technology applications, from more well-known areas of quantum computing and quantum cryptography to lesser-known applications such as quantum communication, quantum-assisted measurement and sensing, and quantum microscopy. This book only assumes that the reader has had the standard courses in quantum mechanics and electromagnetism that are normally taken by physics majors during their sophomore or junior years.
The overall structure of this textbook is divided into four parts. Part I covers background material in elementary quantum mechanics, electromagnetism, optics, solid state physics, and other areas. Since the quantum states required for applications can exist in many types of physical systems, a broad background in many areas of physics is needed. This part of the book aims to ensure that all students have the necessary prerequisites, and to fill any gaps in their prior backgrounds. Part II covers additional topics in quantum mechanics beyond the basics. This includes topics such as interference of quantum states, unusual quantum effects that can be useful for applications, and the quantification of the amount of information carried by a quantum state. Part III is the heart of the book, discussing applications of the material from the previous chapters to real world problems such as high precision measurement, high resolution microscopy, quantum cryptography, and quantum information processing. Part IV covers more practical aspects, discussing detectors, light sources, atomic systems, and other topics that are essential for experimental implementation applications that were described from a more theoretical viewpoint in Part III.
1 Introduction and Preliminaries.- 2 Classical Optics and Optical
Devices.- 3 Quantum Mechanics.- 4 Elements of Solid State and Atomic
Physics.- 5 Light and Matter.- 6 Angular Momentum, Spin, and Two-State
Systems.- 7 Superconductivity.- 8 Classical Information and Classical
Computation.- 9 More on Quantum States.- 10 Quantum Interference.- 11 More
Interference and Measurement Effects.- 12 Quantum Bits and Quantum
Information.- 13 Quantifying Entanglement.- 14 EPR, Bell Inequalities, and
Local Realism.- 15 Gauge Fields and Geometric Phases.- 16 Quantum Computing:
General Considerations.- 17 Quantum Computing: Algorithms.- 18 Quantum
Communication and Quantum Cryptography.- 19 Quantum-Enhanced Metrology and
Sensing.- 20 Quantum Imaging and Related Topics.- 21 Topological Materials.-
22 Optical Sources and Detectors.- 23 Nuclear Magnetic Resonance.- 24 Atomic
and Ionic Systems.- 25 Resonant Cavities and Cavity Quantum Electrodynamics.-
26 Solid State Qubits.- 27 Future Prospects and Guide to Additional Topics.
Format: Paperback / softback, 291 pages, height x width: 235x155 mm, 2 Illustrations, color;
5 Illustrations, black and white; XII, 291 p. 7 illus., 2 illus. in color.
Series: SUMS Readings
Pub. Date: 23-Apr-2025
ISBN-13: 9783031826252
This textbook provides mathematical tools and applies them to study key aspects of data transmission such as encryption and compression. Modern societies are awash with data that needs to be manipulated in many ways: encrypted, compressed, shared between users in a prescribed manner, protected from unauthorized access, and transmitted over unreliable channels. All of these operations are based on algebra and number theory. This textbook covers background topics in arithmetic, polynomials, groups, fields, and elliptic curves required for real-life applications like cryptography, secret sharing, error-correcting, fingerprinting, and compression of information.
The book illustrates the work of these applications using the free GAP computational package. It uses this package to help readers understand computationally hard problems and provide insights into protecting data integrity. This textbook covers a wide range of applications including recent developments, primarily intended for use as a textbook, with numerous worked examples and solved exercises suitable for self-study.
This edition has been thoroughly revised with new topics and exercises, introducing hash functions for properly describing digital signatures, blockchains, and digital currencies in the latest version.
Integers.- Cryptology.- Groups.- Fields.- Polynomials.- Secret Sharing.-
Error-Correcting Codes.- Compression.- Appendix A: GAP.- Appendix B:
Miscellanea.- Solutions to Exercises.- Index.