Provides the first systematic study of geometry and topology of locally symmetric rank one manifolds and dynamics of discrete action of their fundamental groups. In addition to geometry and topology, this study involves several other areas of Mathematics ? from algebra of varieties of groups representations and geometric group theory, to geometric analysis including classical questions from function theory.
This must-have reference provides the first comprehensive study of geometry and topology of locally symmetric rank one manifolds and dynamics of discrete action of their fundamental groups.
1 Riemannian and sub-Riemannian geometries
2 Dynamics of discontinuous groups of homeomorphisms
3 Basics of if-hyperbolic lattices and manifolds
4 Geometrically finite actions in symmetric rank 1 spaces
5 Deformations of locally symmetric spaces
6 Hyperbolic 4-cobordisms and wild dynamics
Bibliography
Index
Bibliograp
This book is in the series
Volume 77 | De Gruyter Expositions in Mathematics
Tropical Mathematics built on Idempotent Semi-Rings and Dioids permits an extension of the usual Linear methods to Non-Linear problems and provides powerful analyzing and computing in Theoretical Physics and Applied Mathematics. Until recently, solutions in mathematics and physics were organized around algebraic structures such as groups, rings, and fields. These techniques are not well-suited to modeling and solving non-linear problems.
This book covers how Idempotent Mathematics when applied appropriately can be a versatile and powerful way to transform non-linear problems into linear ones and can provide solutions to complicated theoretical physics problems.
Basic notations
Part I: Elements of tropical mathematics
Introduction
1 Elements of tropical algebras
2 Elements of tropical topology
3 Elements of tropical analysis
4 Elements of tropical functional analysis
Part II: Some applications of tropical bi-wavelets to signal processing
Introduction
5 Tropical bi-wavelets for Holder exponents and fractal dimensions calculations
6 Tropical bi-wavelets for multi-fractal analysis
7 Tropical bi-wavelets for image processing
Part III: Tropical intervals
Introduction
8 Tropical intervals
9 Tropical inclusion functions
10 Tropical probabilist set inversion
Part IV: Some applications of tropical mathematics in theoretical physics
Introduction
11 Numerical applications with tropical intervals
12 Tropical transforms for theoretical physics
13 Contributions of tropical mathematics to statistical physics
14 (min, +)-Path integral
15 Tropical complex variational calculus
Postface
Introduction
A Tropical intervals numerical implementation
B Tropical probabilist set inversion
C Tropical intervals functions optimization examples
D Tropical intervals linear algebra examples
Bibliography
Index
Language: English
Published/Copyright: 2025
This book is in the series
De Gruyter Proceedings in Mathematics
Wolmer Vasconcelos was one of the giants in the development of Commutative Algebra in the latter half of the twentieth century and the first decades of the twenty-first century. This work collects in one place essays illustrating the important developments of his work particularly in commutative algebra that permits the reader to see the development of his important ideas and how they influence the development of mathematics today.
Essays by experts provide context for understanding the work of Vasconcelos
Focused sections deliver an understanding of collaborative work in Mathematics
Of interest to researchers and graduate students working in all forms of algebra.
Mathematics
Algebra and Number Theory
Mathematics
Geometry and Topology
This book is in the series
De Gruyter Proceedings in Mathematics
The book focuses on the theory of fixed points, which is a foundation for many branches of pure and applied mathematics. Fixed point theorems have been studied in various function spaces. The book contains modern results on these theorems, investigated in generalized spaces such as S-metric spaces, convex metric spaces, and bipolar metric spaces, with applications in medical imaging. The nonlinear analysis presented in the book is valuable for modeling and solving real-world problems. It includes work on specific nonlinear operators and nonlinear fractional integral equations in Banach spaces. Relevant studies are also included on statistical convergence, inventory model modeling, computational techniques for Sentiment Analysis on Twitter Data, and Blood Management applications. The book is intended for young researchers interested in nonlinear analysis, fixed-point theory, and computational techniques.
New results on fixed point theory in generalized metric spaces
New applications in medical images, infectious diseases, Atmospheric Gas Dynamics
Contains new computational techniques like hyperpower iterative methods.
H. K. Nashine is a Professor of Mathematics and Dean of School of Advanced Sciences and Languages at VIT Bhopal University, Bhopal, India. He is a recipient of Fulbright-Nehru Postdoctoral. He has more than 20 years of teaching experience at different level of institutes. He is an active researcher and working on fixed point theory, nonlinear matrix equations and fractional differential and integral equations. He has published more than 200 research papers in various journals which is published by Elsevier, Taylor & Francis, World Scientific, Springer, Hindawi etc, and 10 book chapters in international publications. He has given 15 invited talks in the international/National conferences. He has visited Switzerland, Vietnam, South Korea, Thailand, Brazil and Romania to present research papers. He has completed 4 International and National Projects. He has handled the special issues of International journals as Lead-Editors and editors. He is a reviewer of many journals associated with Elsevier, Springer, Hindawi, Taylor & Francis and MDPI publishers. He is co-author of the book "Approximation Theory, Sequence Spaces and Applications" (Springer, 2022). He has guided 3 PhD students.
Dr. Ranis N. Ibragimov is currently an acquisition editor: Mathematics & Computer Sciences, De-Gruyter Publisher. He was a postdoctoral fellow of McMaster University, Canada after his PhD from University of Waterloo, Canada. Dr Ibragimov was full time faculty of Wenatchee Valley College, USA followed by University of Wisconsin-Parkside, USA. He was a visiting researcher at the Pacific Northwest National Laboratory, Department of Energy, USA. Dr. Ibragimov’s research interests broadly lie in the applications of Mathematical Modeling (including Differential Equations, Analytic and Numerical Methods, Perturbation theory, Bifurcation phenomena, Asymptotic Methods, Data Analysis, and Statistics) to industrial, engineering, and environmental sciences. As a fluid dynamicist, he has worked on geophysical and environmental flows within a complex geometry. His research is numerically oriented and theoretical in nature. Dr. Ibragimov is the editor of several Journals. He is Editor in chief of "Mechanical Engineering Research" , Canadian Center of Science and Education. Dr. Ibragimov is an author of the monograph "Lie Group Analysis of Differential Equations:". He is an author of several books. Dr. Ibragimov is International advisory members of "International Conference on nonlinear and Computational techniques (ICNACT-2024).
Dr. Hemanta Kalita is presently Assistant Professor, Mathematics Division, VIT Bhopal University, Kothri-kalan, Bhopal-Indore Highway, Sehore, Madhya Pradesh, India. Dr. Hemanta Kalita is a Doctorate from Gauhati University under the guidance of Prof Bipan Hazarika. He has an academic experience of 11 years and has worked at various levels up to Assistant Professor. He has 30 publications in peer reviewed International journals with high impact factor and has 2 publications in various International Conferences held in India and abroad. Dr. Kalita has been an expert speaker in various International Conferences and has organized an International Conference (ICNAA-2022). Dr. Kalita was an Invited researcher at Usak University, Turkey, 2023. Dr. Kalita has published an issue in Journal of nonlinear and convex analysis as a guest editor. Currently he is handling several special issues in many high quality Journals. He is working on Function spaces, integration theory and measure theory. Dr. Kalita has research collaborators in several countries of Europe, USA, Asian and Africa.
Mathematics
Numerical and Computational Mathematics
Mathematics
Applied Mathematics
Computer Sciences
Algorithms
Engineering
Civil Engineering
Environmental Engineering
This book will be published on August 18, 2025
This book is in the series
De Gruyter Textbook
This is a book for an undergraduate number theory course, senior thesis work, graduate level study, or for those wishing to learn about applications of number theory to data encryption and security. With no abstract algebra background required, it covers congruences, the Euclidean algorithm, linear Diophantine equations, the Chinese Remainder Theorem, Mobius inversion formula, Pythagorean triplets, perfect numbers and amicable pairs, Law of Quadratic Reciprocity, theorems on sums of squares, Farey fractions, periodic continued fractions, best rational approximations, and Pell’s equation. Results are applied to factoring and primality testing including those for Mersenne and Fermat primes, probabilistic primality tests, Pollard’s rho and p-1 factorization algorithms, and others. Also an introduction to cryptology with a full discussion of the RSA algorithm, discrete logarithms, and digital signatures.
Chapters on analytic number theory including the Riemann zeta function, average orders of the lattice and divisor functions, Chebyshev’s theorems, and Bertrand’s Postulate. A chapter introduces additive number theory with discussion of Waring’s Problem, the pentagonal number theorem for partitions, and Schnirelmann density.
Fully worked out examples, loads of original exercises.
All topics developed from scratch but extended to more advanced topics.
Variety of topics not found in any other single source such as Chebyshev’s theorems, Waring’s problem, RSA algorithm.
Peter D. Schumer is the John C. Baldwin Professor of Mathematics and Natural Philosophy at Middlebury College. He received his B.S and M.S. degrees from Rensselaer Polytechnic Institute and his Ph.D. from University of Maryland. He has held research and teaching positions at UC Berkeley, Stanford, UC San Diego, San Jose State U, and at Doshisha U, Keio U, and ICU in Japan. His main areas of interest are number theory and the history of mathematics. His courses vary from calculus, linear algebra, and the mathematics of games and puzzles to combinatorics, complex analysis, and advanced number theory. He has directed more than fifty senior projects and theses in related areas. His scholarly work has appeared in Mathematika, Journal of Number Theory, Math Horizons, College Mathematics Journal, and elsewhere. He has published two books, Introduction to Number Theory (PWS, 1996) and Mathematical Journeys (Wiley, 2004). His book Fractions ? A Sliver of the Story will be release this year (OUP, 2024). He has also written articles for general audiences on when humans first began to count and the origins of the letter x in algebra. He is a recipient of the Trevor Evans Award from the MAA on an article about the mathematician Paul Erdos (2000). He also teaches courses on the game of go and its cultural significance and has been awarded the national Teacher of the Year award from the American Go Association (2021).
Mathematics
Algebra and Number Theory
Mathematics
Numerical and Computational Mathematics
Computer Sciences
Algorithms
Computer Sciences
IT-Security and Cryptology