Format: Hardback, 380 pages, height x width: 235x155 mm, 32 Illustrations, color;
94 Illustrations, black and white; X, 380 p. 126 illus., 32 illus. in color.,
Pub. Date: 22-May-2025
ISBN-13: 9783031814136
This book consists of a collection of articles dedicated to Valentin Poenaru, on topology and geometry in a broad sense. Poenaru is one of the leading mathematicians whose work had an essential impact on the development of topology in France over the last forty years of the twentieth century. The special topics addressed in this volume include hyperbolic geometry, 3-manifolds, complex and symplectic geometry, differential topology, combinatorial group theory, piecewise-linear topology, algebraic geometry, knots and links, homotopy theory, braid groups, phylogenetics, the history of geometry, and the philosophy of mathematics. This collection of articles, written by well-known researchers, provides a lively insight into a number of current research topics in geometry and topology.
1 Introduction, by Louis Funar and Athanase Papadopoulos.- 2 Primes,
Knots and Po, by Barry Mazur.- 3 A short history of open manifolds related to
complex analytic coordinates, by Dennis Sullivan.- 4 Universal
Spin Teichmuller Theory, I: The action of P(SL(2,Z)) on T ess+, by Robert C.
Penner.- 5 Universal Spin Teichmuller Theory, II: Finite presentation of
P(SL(2,Z)), by Robert C. Penner.- 6 Geometry of Fermats sum of squares, by
Greg McShane and Vlad Sergiescu.- 7 Ends and compactifications in geometric
topology, by Kenichi Ohshika.- 8 Axiomatic phylogenetics, by Vladimir
Turaev.- 9 About the diffeomorphisms of the 3-sphere and a famous theorem of
Cerf (4 = 0), by Fran?ois Laudenbach.- 10 Holomorphic tensors on Vaisman
manifolds, by Liviu Ornea and Misha Verbitsky.- 11 On the topology of
monotone Lagrangians of high dimension, by Mihai Damian.- 12 Kervaire
Problems in Stable Homotopy Theory, by Petr M. Akhmetev.- 13 Lifting generic
maps to embeddings, The double point obstruction, by Sergey A. Melikhov.- 14
Barcodes for continuous maps and a brief introduction to Alternative Morse
Theory, by Dan Burghelea.- 15 A note on the quasi simple filtration of finite
groups, by Francesco Russo.- 16 Lifting maps between graphs to embeddings, by
Alexey Gorelov.- 17 A note on the discriminant loci of a hypersurface of
bi-degree (m, n), by Susumu Tanabe.- 18 Welded graphs, Wirtinger groups and
punctured spheres, by Benjamin Audoux, Jean-Baptiste Meilhan and Akira
Yasuhara.- 19 On geometric representation of L-homology classes, by Friedrich
Hegenbarth and Duan D. Repov.- 20 On elementary invariants of genus one
knots and Seifert surfaces, by Christine Lescop.- 21 On a family of
hyperbolic Brunnian links and their volumes, by Duan D. Repov and Andrei
Yu. Vesnin.- 22 SL(2, Z), les tresses ? trois brins, le tore modulaire et
Aut+(F2), (dapr?s Emil Artin et Jacob Nielsen), by Alexis Marin.- 23 All
the resources of pure mathematics: Mathematical physics and mathematics as
physics, by Arkady Plotnitsky.- 24 The case for absolute geometry, by Victor
Pambuccian.- 25 The Reconstruction of Theaetetus Theory of Ratios of
Magnitudes, by Stelios Negrepontis and Dimitrios Protopapas.- 26 Notice de
travaux, by Valentin Poenaru.- 27 Mathematical Adventures: A letter to Barry
Mazur, by Valentin Poenaru.- 28 Adventures in physics, by Valentin Poenaru.-
29 Dimitru Poenaru, my father, by Valentin Poenaru.- 30 Father Andrei, by
Valentin Poenaru.- 31 The magic summer of 1964, by Valentin Poenaru.- 32 Po,
a mathematician between humanism and science, Corrado Tanasi and Franco
Marchese.
Format: Hardback, 530 pages, height x width: 235x155 mm, 28 Illustrations, color;
36 Illustrations, black and white; X, 530 p. 64 illus., 28 illus. in color.,
Series: Trends in Mathematics
Pub. Date: 06-Jun-2025
ISBN-13: 9783031863189
This festschrift honors Johann A. Makowsky on the occasion of his 75th birthday. Gathering 24 research articles authored by scientific companions, friends, and colleagues, it covers a broad variety of areas to which Johann A. Makowsky made significant contributions himself. These include several areas of mathematical logic and its relevance for Computer Science including Graph polynomials, Algorithms for graph invariants, Algorithms and descriptive complexity theory, complexity of real and algebraic computations, Mathematical logic, Model theory, Design and theory of databases, Logic in computer science and AI and Logic programming. The volume is enriched with 4 biographical essays, and two contributions by the celebrant himself.
- Part I: Personal Notes.- My writing.- Some personal remarks about
Johann A. Makowsky.- The Swiss Connection.- From a Friend and Publisher.-
From graph polynomials to the software industry Lessons from Janos.-
Emancipatory Aspects of Learning and Teaching Mathematics.- Part II:
Scientific Contributions.- Epsilon Calculus Provides Shorter Cut-Free
Proofs.- Variations on a Theme of Makowsky.- Automatic structures and the
problem of natural well-orderings.- On the Counting Complexity of the Cover
Polynomial for Simple Graphs.- Polynomial Threshold Functions of Bounded
Tree-Width: Some Explainability and Complexity Aspects.- Some Equalities are
More Equal than Others.- On the bipartition polynomials for rooted
caterpillars.- NP-completeness by first-order and quantifier-free
interpretations and related topics.- Bounded languages over infinite
alphabets.- Linear Algebraic Quantifiers.- A coarse Tutte polynomial for
hypermaps.- Graph polynomials: some questions on the edge.- Pixelating
relations and functions without adding substructures.- Reflection and
Recurrence.- Provenance Analysis and Semiring Semantics for First-Order
Logic.- Reversify any sequential algorithm.- Gentzen in the 3- and 4-valued
jungle.- Characterizing Data Dependencies Then and Now.- On Consistency of
Graphically Defined Specifications.- The path-bifurcation hierarchy does not
collapse to ??1 in infinite abelian groups.- Data with Logical and
Statistical constraints.- Relating Information and Knowledge.- Science and
Practice of Modelling.- Graph Polynomials and Local Graph Operations.
Format: Paperback 129 pages, height x width: 240x168 mm, 3 Illustrations, color;
1 Illustrations, black and white; X, 129 p. 4 illus., 3 illus. in color.,
Series: Frontiers in Mathematics
Pub. Date: 26-May-2025
ISBN-13: 9783031866333
This monograph presents the work of the authors in metrical theory of continued fractions in the last two decades. The monograph cuts a particular path through this extensive theory and describes the theory in its current form for three families of continued fractions, namely, -continued fractions, N-continued fractions, and generalized Renyi continued fractions. The book systematically lays out the required preliminaries, making the book easy to read. This monograph provides a solid introduction into the theory of continued fractions.
The book is intended for researchers in metrical theory, as well as advanced graduate students and mathematicians interested in this field.
1. Introduction.-
2. -Continued Fraction Expansions.-
3. N-Continued Fractions.-
4. Generalized Renyi Continued Fractions.-
5. Comparing the Efficiency of Different Continued Fraction Algorithms.
Format: Hardback, 321 pages, height x width: 235x155 mm, 59 Illustrations, color;
23 Illustrations, black and white; X, 321 p. 82 illus., 59 illus. in color.
Series: Contributions to Statistics
Pub. Date: 14-Jun-2025
ISBN-13: 9783031697494
This volume on the latest developments in the theory and applications of time series analysis and forecasting comprises a selection of refereed papers presented at the 9th International Conference on Time Series and Forecasting, ITISE 2023, held in Gran Canaria, Spain, July 12-14, 2023. It is divided into several parts that address modern theoretical aspects of time series analysis, advanced econometric methods, time series and machine learning, financial forecasting and risk analysis, and applications to various disciplines, including econometrics and energy research. The broad range of topics and applications presented, including matters of particular relevance for sustainable development, gives readers a modern perspective on the subject.
The ITISE conference series provides a forum for scientists, engineers, educators and students to discuss the latest advances and implementations in the foundations, theory, models and applications of time series analysis and forecasting. It focuses on interdisciplinary research encompassing computer science, mathematics, statistics and econometrics.
- Part I Advanced Econometric Methods.- Banking sector development and economic growth in developing countries. Does the change in the shadow economy matter? A Nonlinear Panel ARDL.- Improving the prediction of Norwegian household consumption by adjusting for temporary fluctuations in dividend income.- Inflation expectations change during the pre-war and war period. A comparison of Ukraine and neighboring economies.- Analysis of diversification in investment portfolios Return and Risk for different time horizons.- Economic Diversity and the Dutch Disease in Angola.- Part II Artificial Intelligence and Time Series.- Increasing the Performance and Plausibility of Machine Learning via Data Analysis Techniques.- Combining Forecasts of Time Series with Complex Seasonality using LSTM-based Meta-Learning.- Bayesian Robust Multivariate Time Series Analysis in Nonlinear Regression Models with Vector Autoregressive and t-distributed Errors.- Forecasting of the F10.7 solar radio index: A Multivariate Deep Learning Approach.- Part III Financial Forecasting and Risk Analysis.- Risk-adjusted Returns of Croatian Largest Manufacturers and Their Determinants.- Usage of portfolio replication in non-life insurance.- Encoding Stock Returns Relationships via Latent Embeddings for Enhanced Portfolio Optimization.- A Measure of Bivariate Long Memories in Financial Time Series with Applications to Granger Causality Networks.- Volatility-inspired s-LSTM cell.- Part IV Theoretical Aspects of Time Series.- Bayesian Analysis of Systemic Risks Distributions.- Empirical function-based time series analysis for high-dimensional ground motion data: A focus on nonstationary and nonlinear phenomena.- Extended Research on Categorical Data Encoding Techniques for Recursive Multi-Step Prediction of Vessel Trajectory.- Part V Time Series Analysis Applications.- Predicting Safety- Critical Events in Traffic Flow Based on Time-Series.- Two-Factor and ARIMA-LS-SVR Models for Forecasting of EUA Futures Prices.- Interest Rate Sensitivity of the largest European Pharmaceutical Companies. An Extension of The Fama and French Five-Factor Model.
Format: Hardback, 871 pages, height x width: 235x155 mm, 14 Illustrations, color;
12 Illustrations, black and white; X, 871 p. 26 illus., 14 illus. in color.,
Series: Birkhauser Advanced Texts / Basler Lehrbucher
Pub. Date: 24-May-2025
ISBN-13: 9783031863653
This book provides a comprehensive and self-contained introduction to the study of the Cauchy problem and unique continuation properties for partial differential equations. Aimed at graduate and advanced undergraduate students, it bridges foundational concepts such as Lebesgue measure theory, functional analysis, and partial differential equations with advanced topics like stability estimates in inverse problems and quantitative unique continuation. By presenting detailed proofs and illustrative examples, the text equips readers with a deeper understanding of these fundamental topics and their applications in mathematical analysis. Designed to serve as both a learning resource and a reference, this book is particularly suited for those pursuing research in mathematical physics, inverse problems, or applied analysis.
1. Introduction.-
Part I: The Sobolev Spaces and the Boundary Value Problems.-
2. Main notations and basic formulas.-
3. Overview of measure theory and functional analysis.-
4. Notes on the distribution theory and Fourier transform.-
5. The Sobolev spaces.-
6. The boundary value problems for secondorder elliptic equations and the Dirichlet to Neumann map.-
Part II: Cauchy Problem for PDEs and Stability Estimates.-
7. The Cauchy problem for the firstorder PDEs.-
8. Real analytic functions.-
9. The Cauchy problem for PDEs with analytic coefficients.-
10. Uniqueness for an inverse problem.-
11. The Hadamard example. Solvability of the Cauchy problem and continuous dependence by the data.-
12. Illposed problems. Conditional stability.-
13. The John stability Theorem for the Cauchy problem for PDEs with analytic coefficients.-
Part III: Carleman Estimates and Unique Continuation Properties.-
14. Carleman estimates: a first look with simple examples and basic applications.-
15. Carleman estimates and the Cauchy problem for operators with ?? coefficients in the principal part.-
16. Carleman estimates for reduced regularity coefficients.-
17. Carleman estimates for secondorder operators with real coefficients in the principal part.-
18. Optimal three sphere and doubling inequality for secondorder elliptic equations.-
19. Miscellanea.
Format: Paperback / softback, 267 pages, height x width: 235x155 mm, X, 267 p.,
Series: Lecture Notes of the Unione Matematica Italiana 29
Pub. Date: 19-May-2025
ISBN-13: 9783031862663
Among several main formulations, the book treats inverse problems with single measurements by Carleman estimates and describes a method for proving the uniqueness and the stability for the first-order transport equations, parabolic equations, and hyperbolic equations. The book gives self-contained derivations of Carleman estimates, which do not rely on any general theory and simplified application method of the Carleman estimates to the inverse problems. Thus, the target audience is graduate students of faculty of sciences and interested graduate students from engineering fields. The book tries to limit the preliminary knowledge to a standard 4-year undergraduate course. In order to master the methodology, we restrict equations within first-order transport equations, parabolic equations and hyperbolic equations, but it is expected to apply the same methods for other evolution equations such as fluid dynamics.
1. How inverse problems appear and what should we study about inverse problems?.-
2. Application of the multiplier method to an inverse wave source problem.-
3. Inverse problems by Carleman estimates for first-order transport equations.-
4. Inverse problems by Carleman estimates for parabolic equations.-
5. Inverse problems by Carleman estimates for hyperbolic equations.-
6. Conditional stability and convergence rates of the Tikhonov regularization.-
7. Other estimates of Carleman type.-
8. Derivation of Carleman estimates for elliptic equations.
Format: Paperback / softback, 559 pages, height x width: 235x155 mm,
13 Illustrations, color; 20 Illustrations, black and white; X, 559 p. 33 illus., 13 illus. in color.,
Series: La Matematica per il 3+2 163
Pub. Date: 24-May-2025
ISBN-13: 9783031871634
The book aims at endowing any student with a survival toolkit to start safely diving into the realm of Calculus of Variations. In summary, the latter is a part of mathematical analysis devoted to minimization/maximization problems. A great effort has been made to present the themes and methods considered in the book in the simplest possible way: the reader will not find here general statements or proofs based on general abstract theories. In contrast, the main focus of the book is on introducing some key concepts "from scratch", by means of simple and meaningful explicit examples (including for instance, the classical isoperimetric and brachistocrone problems, as well as the boundary value problem for harmonic functions). In particular, the book is mainly (but not exclusively) designed to smoothly introduce the reader to the so-called Direct Method of the Calculus of Variations, which is a central concept in the field. Accordingly, a good part of the book is devoted to discussing spaces of weakly differentiable functions (i.e., Sobolev and Lipschitz functions), which are essential tools of the Direct Method.
A long list of problems will guide the student through the study of the subject. Almost all the problems come with their fully detailed solutions. The book is complemented by four appendices, which contribute to making it self-contained, as well as to deepening the study of certain parts.
Despite being designed for students, even the researchers in the field could find a reading of the book profitable, at least for certain parts concerning the properties of Sobolev spaces, functional inequalities of the Sobolev-Poincare type, tricks to handle nonlinear elliptic PDEs, and a gentle introduction to some techniques of modern regularity theory for elliptic PDEs.
1. Tools.-
2. Some One-Dimensional Variational Problems.-
3. Sobolev Spaces.-
4. The Direct Method in Sobolev Spaces.-
5. Lipschitz Functions.-
6. The Direct Method in Lipschitz Spaces.-
7. Excerpts from Regularity Theory.-
8. Solutions to Problems.