Softcover ISBN: 978-1-4704-8177-3
Mathematical Surveys and Monographs
2025; Estimated: 489 pp
Iwasawa theory began in the late 1950s with a series of papers by Kenkichi Iwasawa on ideal class groups in the cyclotomic tower of number fields and their relation to
-adic
-functions. The theory was later generalized by putting it in the context of elliptic curves and modular forms. The main motivation for writing this book, comprised of three volumes, was the need for a total perspective that includes the new trends of generalized Iwasawa theory. Another motivation is an update of the classical theory for class groups taking into account the changed point of view on Iwasawa theory.
Volume 1: explains the theory of ideal class groups, including its algebraic aspect (the Iwasawa class number formula), its analytic aspect (Leopoldt?Kubota
-functions), and the Iwasawa main conjecture, which is a bridge between the algebraic and the analytic aspects.
Volume 2: explains various aspects of the cyclotomic Iwasawa theory of
-adic Galois representations.
Volume 3: presents additional aspects of the Iwasawa theory of -adic Galois deformations.
Graduate students and researchers interested in number theory and arithmetic geometry.
This set contains the following item(s):
Contents
Introduction to cyclotomic Iwasawa theory of elliptic curves
Framework of cyclotomic Iwasawa theory for
-adic Galois representations
Known results on cyclotomic Iwasawa theory for
-adic representations
Appendix A
Contents
Framework on Iwasawa theory for
-adic Galois deformations
Known results on Iwasawa theory for
-adic deformations
Appendix A
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Softcover ISBN: 978-1-4704-8021-9
Expected availability date: October 02, 2025
Mathematical Surveys and Monographs, Volume: 292;
2025; 293 pp
MSC: Primary 53; 49; 58; 35
This book provides a systematic treatment of the main results on the Morse index of minimal submanifolds of Riemannian manifolds. After an introductory chapter reviewing the necessary material, this book provides a survey of the basic properties of the Morse index, as well as a large number of examples of minimal submanifolds with the corresponding calculation of their Morse index. The analysis of minimal submanifolds and their index in the cases when the ambient manifold is the Euclidean space, sphere, real and complex projective spaces are analyzed in detail; many other classes of ambient varieties are also studied. The text also includes some of the main open problems in the theory. Potential readers of this book are graduate students and researchers in geometric analysis.
Graduate students and researchers interested in differential geometry.
Table of Contents
Foundations
Variation formulas. Stability. Index and nullity
Complete minimal submanifolds of non-negatively curved Riemannian manifolds
Index of minimal submanifolds of Euclidean spaces
Index of minimal submanifolds of spheres, real projective spaces, product of spheres and elliptic Berger spheres
Index of minimal submaniolds of Kahler manifolds
Glossary
Bibliography
Index
Index of authors
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Handbook of Statistics Volume 53 -
September 1, 2025
Hardback ISBN: 9780443314223
Statistics in Industry and Government covers industrial quality control and high-class quality maintenance in products. The book aims to cover as many applications that use statistics as an underlying tool in bringing the best quality products and industrial designs. Chapters in this new release include Analysis of Official Time Series with Ecce Signum, an R Package for Multivariate Signal Extraction and Forecasting, The Maturity Structure of Public Debt: A Granular Approach Using Indian Data, Harnessing the power of spherical intersection: A less arbitrary unsupervised learning method applied to pattern recognition within financial data, and much more.
Other chapters in this release include The Use of Causal Inference with Structural Models in Industry, MSME Statistics in India, The Importance of Accurate, Timely, Credible Crime Data to Inform Crime and Justice Policy, Combining Information from Multiple Sources in Official Statistics, Active Learning of Computer Experiment with both Quantitative and Qualitative Inputs, On the use of machine learning methods for missing data problems, Optimal Experimental Planning for Experiments Based on Coherent Systems with Industrial Applications, and more.
1. Analysis of Official Time Series with Ecce Signum, an R Package for Multivariate Signal Extraction and Forecasting
Tucker Sprague McElroy and James Livsey
2. The Maturity Structure of Public Debt: A Granular Approach Using Indian Data
Chetan Ghate, Piyali Das and Subhadeep Halder
3. Harnessing the power of spherical intersection: A less arbitrary unsupervised learning method applied to pattern recognition within financial data
Michel Ferreira Cardia Haddad
4. The Use of Causal Inference with Structural Models in Industry
Takashi Isozaki
5. MSME Statistics in India
Poonam Munjal, Palash Baruah and sanjib pohit
6. The Importance of Accurate, Timely, Credible Crime Data to Inform Crime and Justice Policy
Alex R. R. Piquero
7. Combining Information from Multiple Sources in Official Statistics
Changbao Wu
8. Active Learning of Computer Experiment with both Quantitative and Qualitative Inputs
Chunfang Devon Lin, Xinwei Deng and Anita Shahrokhian
9. On the use of machine learning methods for missing data problems
Sixia Chen
10. Optimal Experimental Planning for Experiments Based on Coherent Systems with Industrial Applications
Hon Keung Tony Ng, Erhard Cramer and Yang Yu
11. An overview of models for one-shot device testing data analysis.
Man Ho Ling
12. TBA
Qing Yin
13. TBA
Ram C. Tiwari, JIXIAN WANG and Hongtao Zhang
14. Statistical Innovation: Transforming Pharmaceutical Research and Development
Pandurang M. Kulkarni, Wei Shen, Demissie Alemayehu and Yongming Qu
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October 1, 2025
Paperback ISBN: 9780443223433
Expected release date: October 1, 2025
Dynamic Modelling of Time-to-Event Processes covers an alternative dynamic modelling approach for studying time-to-event processes. This innovative approach covers some key elements, including the Development of continuous-time state of dynamic time-to-event processes, an Introduction of an idea of discrete-time dynamic intervention processes, Treating a time-to-event process operating/functioning under multiple time-scales formulation of continuous and discrete-time interconnected dynamic system as hybrid dynamic time-to-event process, Utilizing Euler-type discretized schemes, developing theoretical dynamic algorithms, and more.
Additional elements of this process include an Introduction of conceptual and computational state and parameter estimation procedures, Developing multistage a robust mean square suboptimal criterion for state and parameter estimation, and Extending the idea conceptual computational simulation process and applying real datasets.
1. Some Latent Dynamic Structural Elements in Time-to-Event Processes
1.1. Introduction
1.2. Preliminary Concepts and Results in Survival and Reliability analysis
1.3. Motivations for Continuous time Dynamic of Time-to-Event Processes
1.4. Illustration Existing Dynamic Model of Time-to-Event-Process
1.5. Basic Components and functions of Hybrid Dynamic Process
1.6. Notes and Comments
2. Linear Deterministic Hybrid Dynamic Modeling of Time-to-event Processes (LDHDM)
2.1. Introduction
2.2. Linear Continuous-time hybrid dynamic model Formulation
2.3. Linear Discrete-time hybrid dynamic Model Formulation
2.4. Fundamental Results for Continuous-time Dynamic processes
2.5. A Few Results for Discrete-time Hybrid Iterative Processes
2.6. Estimation of Survival and Risk Rate Parameters
2.7. Estimation of Survival and Risk States
2.8. Analysis of Multiple Censored times between Consecutive Failure Times
2.9. Notes and Comments
3. Conceptual Computational and Simulation Algorithms - LDHDM
3.1. Introduction3.2. Conceptual computational parameter and state estimation schemes
3.3. Conceptual computational simulation algorithms
3.4. Simulation Algorithm for Interconnected Hybrid Dynamic Process
3.5. Notes and Comments
4. Nonlinear Deterministic Interconnected Hybrid Dynamic Modeling for Time-to-Event Processes - INHDMTTEP
4.1. Introduction
4.2. Basic Concepts and Modifications
4.3. Motivation for Nonlinear Formulation with Illustrations
4.4. Formulation of Large-scale Nonlinear Hybrid Dynamic Model
4.5. Derivation of Theoretical Interconnected Discrete-time Dynamic Algorithm ? IDATTEDS
4.6. Theoretical Parameters and State Estimations
4.6.1. Theoretical Parameter Estimations of Multiple Censored and Admittance between Two Consecutive Failure Times
4.6.2. Parameter and State Estimation for Totally Discrete-time Hybrid Dynamic Model
4.6.3. Modified Local lagged Adaptive Generalized Method of Moments (LLGMM) Parameter and State Estimation Schemes
4.7. Change-point Data Analysis Problem
4.8. Notes and Comments
5. Conceptual Computational and Simulation Algorithms for INHDMTTEP
5.1. Introduction
5.2. Data Collection and Coordination with Iterative Processes
5.3. Data Decomposition, Reorganization, and Aggregation Process
5.4. Conceptual Computational Parameter and State Estimation Schemes - IDATTEDS
5.5. Conceptual Computational State Simulation Schemes ? IDATTEDS
5.6. Modified LLGMM Conceptual Computational Simulation Schemes and Algorithms
5.7. Notes and Comments
6. Stochastic Hybrid Dynamic Modeling for Time-to-event Processes - SIHDMTTEP
6.1. Introduction
6.2. Motivation and Formulation of Stochastic Hybrid Dynamic Model
6.3. Fundamental Results for Stochastic Hybrid Dynamic Processes
6.4. Theoretical Conceptual Parameter and State Estimation Schemes ? SIDANTTEDS
6.5. Fundamental Conceptual Computational Discrete-time Data Observation Systems
6.6. Development of Discrete time Conceptual Computational Dynamic State and Parameter Estimation Problem
6.7. Theoretical Parameter Estimations of Multiple Censored and Admittance between Two Consecutive Failure Times
6.8. Modified LLGMM conceptual computational parameter and state estimation.
6.9. Change-point Data Analysis Problem6.10. Notes and Comments
7. Conceptual Computational and Simulation Algorithms for SIHDMTTEP
7.1. Introduction
7.2. Data Collection Coordination with Iterative Processes
7.3. Data Decomposition, Reorganization, and Aggregation Process
7.4. Conceptual Computational Parameter and State Estimation Schemes ? SIDANTTTEDS
7.5. Conceptual Computational State Simulation Schemes ? SIDANTTEDS
7.6. Modified LLGMM Conceptual Computational Simulation Schemes Algorithms
7.7. Notes and Comment
8. Application to Time-to-Event Datasets
8.1. Introduction
8.2. Case study: Application of IDATTEDS to Time-to-Event Datasets
8.3. Case study: Application of Modified LLGMM to Time-to-Event Datasets
8.3.1. Application of Deterministic Modified LLGMM to Time-to-Event Datasets
8.3.2. Application of Stochastic Modified LLGMM to Time-to-Event Datasets
8.4. Notes and Comments
9. Statistical Comparative Analysis with Existing Methods
9.1. Introduction
9.2. Comparison of LHDDM with Existing Methods
9.3. Comparison of IDATTEDS with Existing Methods
9.4. Comparison of Modified LLGMM with Existing Methods
9.4.1. Comparison of Deterministic Modified LLGMM with Existing Methods
9.4.2. Comparison of Stochastic Modified LLGMM with Existing Methods
9.5. Notes and Comments
10. Case Studies
10.1. Introduction
10.2. Adoption and Replacement for Succeeding Generation of High Technology Products
10.3. Application of Time-to-event Processes for Evaluating Demand Side Management
10.4. Generalized Network Externality Process
10.5. Application of Time-to-event Processes to Marketing Decision Making
10.6. Role and Scope Mathematical Sciences
10.7. Baseline and Marshall-Olkin-type Modified Distributions
10.8. Notes and Comments
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This memoir is devoted to the theory of vector-valued modular forms for orthogonal groups of signature (2,n). Our purpose is multi-layered: (1) to lay a foundation of the theory of vector-valued orthogonal modular forms; (2) to develop some aspects of the theory in more depth such as geometry of the Siegel operators, filtrations associated to 1-dimensional cusps, decomposition of vector-valued Jacobi forms, square integrability etc; and (3) as applications derive several types of vanishing theorems for vector-valued modular forms of small weight. Our vanishing theorems imply in particular vanishing of holomorphic tensors of degree less than n/2?1 on orthogonal modular varieties, which is optimal as a general bound. The fundamental ingredients of the theory are the two Hodge bundles. The first is the Hodge line bundle which already appears in the theory of scalar-valued modular forms. The second Hodge bundle emerges in the vector-valued theory and plays a central role. It corresponds to the non-abelian part O(n,R) of the maximal compact subgroup of O(2,n). The main focus of this monograph is centered around the properties and the role of the second Hodge bundle in the theory of vector-valued orthogonal modular forms.
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Paperback
The volume is part of the Surveys of Modern Mathematics
In mathematics, anything exceptional is of special interest, and one of the most pronounced cases of exceptional objects is the famous Killing-Cartan classification of simple Lie groups (or algebras) into 4 infinite series and a finite set of 5 exceptional groups. That a very similar classification of objects occurs in such far-apart areas as singularities of surfaces, graphs and representations turns out to be not just coincidence, and is discussed in the book. One main objective is a discussion of the geometry of exceptional homogeneous spaces which is treated in great detail. In addition the book sketches many applications of the exceptional groups in theoretical (particle) physics as well as in algebraic geometry.
The reader may look forward to seeing the fundamental particles of the standard model as elements of the tensor product of the four real division algebras (the real and complex numbers, the quaternions and octonions), sometimes referred to as the Dixon algebra, which just happens to have the right number of complex dimensions ? 32 ? to accommodate one generation of the standard model (Dixonfs theory). The more elaborate theory of supergravity can also be described using octonions (Hughes' theory), and via compactification of the 11-dimensional supergravity, non-compact homogeneous spaces which are the non-compact duals of some of the compact spaces described earlier in the book appear. This culminates in a magic pyramid, an incredible extension of the famous magic squares appearing in the theory.
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Series:
Princeton Series in Applied Mathematics
This book explains gradient-based stochastic optimization, exploiting the methodologies of stochastic approximation and gradient estimation. Although the approach is theoretical, the book emphasizes developing algorithms that implement the methods. The underlying philosophy of this book is that when solving real problems, mathematical theory, the art of modeling, and numerical algorithms complement each other, with no one outlook dominating the others.
The book first covers the theory of stochastic approximation including advanced models and state-of-the-art analysis methodology, treating applications that do not require the use of gradient estimation. It then presents gradient estimation, developing a modern approach that incorporates cutting-edge numerical algorithms. Finally, the book culminates in a rich set of case studies that integrate the concepts previously discussed into fully worked models. The use of stochastic approximation in statistics and machine learning is discussed, and in-depth theoretical treatments for selected gradient estimation approaches are included.
Numerous examples show how the methods are applied concretely, and end-of-chapter exercises enable readers to consolidate their knowledge. Many chapters end with a section on gPractical Considerationsh that addresses typical tradeoffs encountered in implementation. The book provides the first unified treatment of the topic, written for a wide audience that includes researchers and graduate students in applied mathematics, engineering, computer science, physics, and economics.