Format: Paperback / softback, 163 pages, height x width: 235x155 mm, 43 Illustrations, color;
44 Illustrations, black and white; XIII, 163 p. 87 illus., 43 illus. in color., 1 Paperback / softback
Series: SpringerBriefs in Physics
Pub. Date: 26-Jul-2025
ISBN-13: 9783031865435
This book derives, solves, and assesses the Langevin Stochastic Equations (LSE) as a tool for treating turbulent flows. Previous work has demonstrated the LSE's ability to successfully describe non-geophysical turbulent flows. However, this book specifically focuses on geophysical flows. Chapter I addresses the modeling of oceanic mesoscales (M) and sub-mesoscales (SM), while Chapter II discusses vertical mixing.
The target audience for this book is advanced students and researchers interested in future climate change and the crucial role played by the ocean. One of the main challenges in describing oceanic M and SM is that they are governed by non-linear interactions for which no satisfactory model exists. Despite the unsuccessful attempts to describe non-linearity using the traditional Navier-Stokes Equations (NSE), heuristic models continue to be used. This has created a dilemma: while future climate projections need to be predictive, the heuristic treatment of M and SM lacks predictive power, leading to an internal inconsistency.
The primary goal of this book is to demonstrate that the transition from NSE to LSE resolves this inconsistency, paving the way for a fully predictive treatment of M and SM. This advancement is crucial for providing future climate predictions with the credibility they require.
Mesoscales and Sub-mesoscales.- Vertical mixing.
Format: Hardback, 717 pages, height x width: 235x155 mm, X, 717 p., 1 Hardback
Series: Springer Monographs in Mathematics
Pub. Date: 25-Jul-2025
ISBN-13: 9783031860423
In the second edition we do not only correct errors, update references and improve some of the proofs of the text of the first edition, but also add a new chapter on singularities in arbitrary characteristic. We give an overview of several aspects of singularities of algebraic varieties and formal power series defined over a field of arbitrary characteristic (algebraically closed or not). Almost all of the results presented here appeared after the publication of the first edition and some results are new.
In particular, we treat, in arbitrary characteristic, the classical invariants of hypersurface singularities, and we review results on the equisingularity of plane curve singularities, on the classification of parametrizations of plane branches, and on hypersurface and complete intersection singularities with small moduli. Moreover, we discuss and prove determinacy and semicontinuity results of families of ideals and matrices of power series parametrized by an arbitrary Noether base scheme, which are used to prove open loci properties for several singularity invariants. The semicontinuity has surprising applications in the computation of local standard bases of zero dimensional ideals, which are by magnitudes faster than previously known methods.
The chapter contains two appendices. One is by Dmitry Kerner on large submodules within group orbits, which relates to determinacy criteria for singularities in very general contexts. It is focused on methods applicable to a broad class of fields of arbitrary characteristic, while before the theory was mainly restricted to zero characteristic. The second appendix is by Ilya Tyomkin and deals with the geometry of Severi varieties, mainly on toric varieties. It discusses the breakthrough solution to the problem on the irreducibility of Severi varieties of the plane in arbitrary characteristic, with a focus on the characteristic free approach based on tropical geometry.
We try to be self-contained and give proofs whenever possible. However, due to the amount of material, this is not always possible, and we then give precise references to the original sources.
1 Singularity Theory.- 2 Local Deformation Theory.- 3 Singularities in
Arbitrary Characteristics.- Appendix A: Sheaves.- Appendix B: Commutative
Algebra.- Appendix C: Formal Deformation Theory.
Format: Paperback / softback, 418 pages, height x width: 226x189 mm, X, 418 p., 1 Paperback / softback
Series: Mathematics Study Resources 19
Pub. Date: 08-Jul-2025
ISBN-13: 9783662709986
Is mathematics free of contradictions? Are there truths beyond what can be proven? Is it possible to encode our mathematical knowledge into a single number?
Modern mathematical logic of the twentieth century provides astonishing answers to these questions.
This book takes you on a journey through the core areas of mathematical logic, leading to the limits of mathematics. The covered topics include the history of mathematical logic, formal systems, axiomatic number theory and set theory, proof theory, Godel's incompleteness theorems, computability theory, algorithmic information theory, and model theory.
The book contains numerous two-color illustrations and more than 70 exercises (with solutions available on the author's website). This translation is based on the third edition of the original German book.
1 Historic Notes.- 2 Formal Systems.- 3 Foundations of Mathematics.- 4
Peoof Thory.- 5 Computability Theory.- 6 Algorithmic Information Theory.-
Model Theory.
Format: Hardback, 287 pages, height x width: 235x155 mm, 5 Illustrations, color; 15 Illustrations, black and white; X, 287 p. 20 illus., 5 illus. in color., 1 Hardback
Series: Trends in Mathematics
Pub. Date: 23-Aug-2025
ISBN-13: 9783031898563
This volume collects papers based on lectures given at the XLI Workshop on Geometric Methods in Physics, held in Bialystok, Poland in July 2024 as well as extended abstracts of minicourses presented during the XIII School on Geometry and Physics. These chapters provide readers an overview of cutting-edge research in quantum field theories, infinite-dimensional groups, integrable systems, noncommutative geometry, and a wide variety of other areas. Specific topics include:
? Graded structures
? Lie algebra structures
? Quasicrystals
? Sigma models
? Barycentric algebras
? Nijenhuis geometry
Geometric Methods in Physics XLI will be a valuable resource for mathematicians and physicists interested in recent developments at the intersection of these areas.
Part I: Workshop Lectures.
Chapter 1 Scattering in phase space quantum
mechanics the Born approximation.
Chapter 2 The Schwarzschilds solution
and Machs principle.
Chapter 3 Geometric flows, entropy and nonlinear
electrodynamics.
Chapter 4 Weird, Odd, Generalized.
Chapter 5 Restricted
orbits of closed range operators.
Chapter 6 On certain Lie algebra
structures.
Chapter 7 Darboux transformations applied to graphene in
magnetic fields.
Chapter 8 Variants of asymptotics in the
Belinski-Khalatnikov-Lifshitz scenario.
Chapter 9 Poisson structures in the
Banach setting: comparison of different approaches -2.
Chapter 10
Q-manifolds and sigma models.
Chapter 11 Quasicrystal problem - on rigidity
of non-periodic structures from statistical mechanics point of view.
Chapter
12 Qusicrystals in Vernam cipher.
Chapter 13 Explicit Formulae for
Deformation Quantization with Separation of Variables of G2,4(C) .
Chapter
14 On the conformal Lie superalgebras K(1; N = 1; 2; 3) and related
semi-supersymmetric integrable systems.
Chapter 15 Notes on equivalent
formulations of Hamiltonian dynamics on multicotangent bundles.
Chapter 16
Star Product and Star Zeta Function.
Chapter 17 Partitions of unity and
barycentric algebras.- Part II: Abstracts of Lectures at XIII School on
Geometry and Physics.
Chapter 18 Nijenhuis Geometry and its Applications.-
Chapter 19 Generalized geometry in relation to physics and mechanics -3 .-
Chapter 20 Barycentric algebras convexity and order.
Format: Hardback, 207 pages, height x width: 235x155 mm, 23 Illustrations, color;
68 Illustrations, black and white; XIII, 207 p. 91 illus., 23 illus. in color., 1 Hardback
Series: Statistics for Social and Behavioral Sciences
Pub. Date: 26-Jul-2025
This book presents foundational concepts, essential principles, and practical applications of Item Response Theory (IRT). It provides a structured survey of diverse models that have been put forth, emphasizing both their differences and commonalities.
The main focus is on modern latent trait theory models which provide measurement tools that clearly separate between person abilities and item parameters. The topics covered include the binary Rasch model, its extensions and alternative binary models, ordinal models and their extensions that account for response styles, the thresholds model, classical test theory, response models for count data, differential item functioning, and explanatory item response models. Tree-based item response models, typically not found in classical IRT textbooks, are also addressed.
Applications of the models are illustrated on several data sets from differing areas, showing how models can be fitted and compared. All examples have been computed using R. Code snippets are provided, and the full R code for most of the examples is available online.
The book is aimed at graduate students, applied statisticians, and researchers working in psychometrics, educators, and anyone curious about modeling strategies that enhance the precision and validity of their measurement tools. It serves as an introductory guide for beginners while also providing a resource for those seeking an overview of the plethora of available IRT models.
Preface.- Introduction.- The Binary Rasch Model.- Extensions of the
Rasch Model and Alternative Binary Models.- Ordinal Models.- Extended Ordinal
Models Accounting for Response Styles.- The Thresholds Model a Common
Framework for Discrete and Continuous Responses.- Classical Test Theory.-
Response Models for Count Data.- Tree-Based Item Response Models.-
Differential Item Functioning.- Explanatory Item Response Models.- R
Packages.- Examples.- Bibliography.
Format: Paperback / softback, 458 pages, height x width: 254x178 mm
Series: Graduate Studies in Mathematics
Pub. Date: 25-Aug-2025
ISBN-13: 9781470480264
The theory of positive or completely positive maps from one matrix algebra to another is the mathematical theory underlying the quantum mechanics of finite systems, as well as much of quantum information and computing. Inequalities are fundamental to the subject, and a watershed event in its development was the proof of the strong subadditivity of quantum entropy by Lieb and Ruskai. Over the next 50 years, this result has been extended and refined extensively. The development of the mathematical theory accelerated in the 1990s when researchers began to intensively investigate the quantum mechanical notion of ""entanglement"" of vectors in tensor products of Hilbert spaces. Entanglement was identified by Schrodinger as a fundamental aspect of quantum mechanics, and in recent decades questions about entanglement have led to much mathematical progress. What has emerged is a beautiful mathematical theory that has very recently arrived at a mature form. This book is an introduction to that mathematical theory, starting from modest prerequisites. A good knowledge of linear algebra and the basics of analysis and probability are sufficient. In particular, the fundamental aspects of quantum mechanics that are essential for understanding how a number of questions arose are explained from the beginning.
Hilbert space basics
Tensor products of Hilbert spaces
Monotonicity and convexity for operators
von Neumann algebras on finite dimensional Hilbert spaces
Positive linear maps and quantum operators
Some basic trace function inequalities
Fundamental entropy inequalities
Consequences and refinements of SSA
Quantification of entanglement
Convexity, concavity and monotonicity
Majorization methods
Tomita-Takesaki theory and operator inequalities
Convex geometry
Complex interpolation
Bibliography
Index
Format: Hardback, 424 pages, Worked examples or Exercises
Pub. Date: 30-Sep-2025
ISBN-13: 9781009580694
Ideal for students and researchers in the quantitative sciences, this book provides an authoritative and approachable account of probability theory, written by leading researchers in the field. Modern applications are also developed, giving readers an appreciation of important research topics such as statistical mechanics and information theory.
Based on the long-running Probability Theory course at the Sapienza University of Rome, this book offers a fresh and in-depth approach to probability and statistics, while remaining intuitive and accessible in style. The fundamentals of probability theory are elegantly presented, supported by numerous examples and illustrations, and modern applications are later introduced giving readers an appreciation of current research topics. The text covers distribution functions, statistical inference and data analysis, and more advanced methods including Markov chains and Poisson processes, widely used in dynamical systems and data science research. The concluding section, 'Entropy, Probability and Statistical Mechanics' unites key concepts from the text with the authors' impressive research experience, to provide a clear illustration of these powerful statistical tools in action. Ideal for students and researchers in the quantitative sciences this book provides an authoritative account of probability theory, written by leading researchers in the field.
1. Introduction to probability;
2. Probability distributions;
3. Law of large numbers and central limit theorem;
4. Large deviations;
5. Statistical inference and experimental data analysis;
6. Multivariate and correlated experimental data;
7. Random walkers;
8. Generating functions and chain reactions;
9. Recurrent events;
10. Markov chains;
11. Numerical simulations;
12. Correlated events;
13. Continuous time Markov processes;
14. Entropy, Probability, Statistical Mechanics.