Format: Paperback / softback, 274 pages, height x width: 235x155 mm, 130 Illustrations, color; 14 Illustrations, black and white; X, 260 p. 119 illus., 108 illus. in color., 1 Paperback / softback
Series: Springer Undergraduate Mathematics Series
Pub. Date: 10-Oct-2024
ISBN-13: 9783031658198
This text presents selected applications of discrete-time stochastic processes that involve random interactions and algorithms, and revolve around the Markov property. It covers recurrence properties of (excited) random walks, convergence and mixing of Markov chains, distribution modeling using phase-type distributions, applications to search engines and probabilistic automata, and an introduction to the Ising model used in statistical physics. Applications to data science are also considered via hidden Markov models and Markov decision processes. A total of 32 exercises and 17 longer problems are provided with detailed solutions and cover various topics of interest, including statistical learning.
1. A Summary of Markov Chains.-
2. Phase-Type Distributions.-
3. Synchronizing Automata.-
4. Random Walks and Recurrence.-
5. Cookie-Excited Random Walks.-
6. Convergence to Equilibrium.-
7. The Ising Model.-
8. Search Engines.-
9. Hidden Markov Model.-
10. Markov Decision Processes.
Format: Hardback, 301 pages, height x width: 235x155 mm, 57 Illustrations, color; 10 Illustrations, black and white; Approx. 300 p., 1 Hardback
Series: SEMA SIMAI Springer Series 37
Pub. Date: 15-Oct-2024
ISBN-13: 9783031627149
This book presents recent research results from a selection of the talks presented in the international symposium New Trends in Approximation and Applications, held at Oujda, Morocco, in June 2022. The various chapters describe developments in approximation and its different applications including approximation methods in Numerical Analysis, curves and surfaces in CAGD, interpolation and smoothing, shape modelling and computational topology, subdivision schemes and applications, wavelets, and multiresolution methods. The book is addressed to researchers in all of these areas as well as in general mathematical modelling.
Format: Hardback, 195 pages, height x width: 235x155 mm, 4 Illustrations, color; 25 Illustrations, black and white; X, 195 p. 22 illus., 1 Hardback
Series: Trends in Mathematics
Pub. Date: 21-Oct-2024
ISBN-13: 9783031649905
This volume presents recent advances and open problems in the cross section of infinite-dimensional systems theory and the modern treatment of PDEs. Chapters are based on talks and problem sessions from the first Workshop on Systems Theory and PDEs (WOSTAP), held at TU Bergakademie Freiberg in July 2022. The main topics covered include:
Differential algebraic equations Port-Hamiltonian systems in both finite and infinite dimensions Highly nonlinear equations related to elasticity/plasticity Modeling of thermo-piezo-electromagnetism
On some Impedance Boundary Conditions for a Thermo-Piezo-Electromagnetic
System.- A Note on Some Non-Local Boundary Conditions and their Use in
Connection with Beltrami Fields.- Spectral Theory for Schrodinger Operators
on Compact Metric Graphs with AND Couplings: A Survey.- Asymptotic
Stability of port-Hamiltonian Systems.- Port-Hamiltonian Formulation of Oseen
Floes.- On the equivalence of geometric and descriptor representations of
linear port-Hamiltonian systems.- On Differential-Algebraic Equations with
Bounded Spectrum in Banach Spaces.- BIBO stability for funnel control:
semilinear internal dynamics with unbounded input and output operators.- On
checking Lp-admissibility for parabolic control systems.
Format: Paperback / softback, 290 pages, height x width: 235x155 mm, 23 Illustrations, color; 16 Illustrations, black and white; X, 290 p. 38 illus., 23 illus. in color., 1 Paperback / softback
Series: Compact Textbooks in Mathematics
Pub. Date: 06-Oct-2024
ISBN-13: 9783031660887
This book covers the basics of numerical methods. Avoiding the definition-theorem-proof style, it instead focuses on numerical examples and simple pseudo-codes.
The text begins with a chapter on floating point arithmetic before moving on to discuss norms, conditions numbers, solutions of systems of equations, the least squares problem, eigenvalue problems, interpolation, numerical integration, ordinary differential equations, optimization (including a detailed case study), and practical error estimations. Exercises (partly in MATLAB) are provided at the end of each chapter. Suitable for readers with minimal mathematical knowledge, the book not only offers an elementary introduction to numerical mathematics for programmers and engineers but also provides supporting material for students and teachers of mathematics.
Floating Point Arithmetic.- Norms, Condition Numbers.- Solving Systems
of Linear Equations.- The Least Squares Problem.- Eigenvalue Problems.-
Interpolation.- Nonlinear Equations and Systems.- Numerical Integration.-
Ordinary Differential Equations.- Optimization.- Practical Error Estimation.
Format: Hardback, 265 pages, height x width: 235x155 mm, 148 Illustrations, color; 51 Illustrations, black and white; X, 250 p. 80 illus., 32 illus. in color., 1 Hardback
Pub. Date: 30-Sep-2024
ISBN-13: 9783031660849
This book describes how Bayesian methods work. Aiming to demystify the approach, it explains how to parameterize and compare models while accounting for uncertainties in data, model parameters and model structures. Bayesian thinking is not difficult and can be used in virtually every kind of research. How exactly should data be used in modelling? The literature offers a bewildering variety of techniques (Bayesian calibration, data assimilation, Kalman filtering, model-data fusion, ). This book provides a short and easy guide to all these approaches and more. Written from a unifying Bayesian perspective, it reveals how these methods are related to one another. Basic notions from probability theory are introduced and executable R codes for modelling, data analysis and visualization are included to enhance the books practical use. The codes are also freely available online.
This thoroughly revised second edition has separate chapters on risk analysis and decision theory. It also features an expanded text on machine learning with an introduction to natural language processing and calibration of neural networks using various datasets (including the famous iris and MNIST). Literature references have been updated and exercises with solutions have doubled in number.
1. Science and Uncertainty.-
2. Bayesian Inference.-
3. Assigning a Prior Distribution.-
4. Assigning a Likelihood Function.-
5. Deriving the Posterior Distribution.-
6. Markov Chain Monte Carlo Sampling (MCMC).-
7. Sampling from the Posterior Distribution by MCMC.-
8. MCMC and Multivariate Models.-
9. Bayesian Calibration and MCMC: Frequently Asked Questions.-
10.After the Calibration: Interpretation, Reporting, Visualisation.-
11. Model Ensembles: BMC and BMA.-
12. Discrepancy.-
13. Approximations to Bayes.-
14.Thirteen Ways to Fit a Straight Line.-
15. Gaussian Processes and Model Emulation.-
16. Graphical Modelling.-
17. Bayesian Hierarchical Modelling.-
18. Probabilistic Risk Analysis.-
19. Bayesian Decision Theory.-
20. Linear Modelling: LM, GLM, GAM and Mixed Models.-
21. Machine Learning.-
22. Time Series and Data Assimilation.-
23. Spatial Modelling and Scaling Error.-
24. Spatio-Temporal Modelling and Adaptive Sampling.-
25. What Next?.
Format: Hardback, 851 pages, height x width: 235x155 mm, 1 Illustrations, black and white; XX, 800 p., 1 Hardback
Series: Algebra and Applications 31
Pub. Date: 01-Oct-2024
ISBN-13: 9789819752836
This book provides an introduction to the foundations and recent developments in commutative algebra. A look at the contents of the first five chapters shows that the topics covered are those usually found in any textbook on commutative algebra. However, this book differs significantly from most commutative algebra textbooks: namely in its treatment of the DedekindMertens formula, the (small) finitistic dimension of a ring, Gorenstein rings, valuation overrings, the valuative dimension, and the Nagata rings. Chapter 6 goes on to present w-modules over commutative rings, as they are most commonly used in torsion theory and multiplicative ideal theory. Chapter 7 deals with multiplicative ideal theory over integral domains. Chapter 8 collects various results of pullbacks, especially Milnor squares and D + M constructions, which are probably the most important example-generating machines. In Chapter 9, coherent rings of finite weak global dimensions are probed, and the local ring of weak global dimension two is elaborated by combining homological tricks and methods of star operation theory. Chapter 10 is devoted to the Grothendieck group of a commutative ring. In particular, the BassQuillen problem is discussed. Finally, Chapter 11 introduces relative homological algebra, especially where the related notions of integral domains appearing in classical ideal theory are defined and studied using the class of Gorenstein projective modules. In Chapter 12, in this new edition, properties of cotorsion theories are introduced and show, for any cotorsion pair, how to construct their homology theory. Each section of the book is followed by a selection of exercises of varying difficulty. This book appeals to a wide readership, from graduate students to academic researchers interested in studying commutative algebra.
Basic Theory of Rings and Modules.- Several Classical Module Classes in
the Module Category.- Homological Methods.- Basic Theory of Noetherian
Rings.- Extensions of Rings.- w-Modules over Rings.- Multiplicative Ideal
Theory over Integral Domains.- Structural Theory of Milnor Squares.- Coherent
Rings with Finite Weak Global Dimension.- Grothendieck Groups of Rings.-
Relative Homological Algebra.- Cotorsion Theory.
Format: Hardback, 470 pages, height x width: 235x155 mm, X, 460 p., 1 Hardback
Series: Operator Theory: Advances and Applications 298
Pub. Date: 28-Sep-2024
ISBN-13: 9783031649820
Other books in subject:
The present monograph serves as a natural extension of the prior 2-volume monograph with the same title and by the same authors, which encompassed findings up until 2014. This four-volume project encapsulates the authors decade-long research in the trending topic of nonstandard function spaces and operator theory.
One of the main novelties of the present book is to develop the extrapolation theory, generally speaking, in grand Banach function spaces, and to apply it for obtaining the boundedness of fundamental operators of harmonic analysis, in particular, function spaces such as grand weighted Lebesgue and Lorentz spaces, grand variable exponent Lebesgue/Morrey spaces, mixed normed function spaces, etc. Embeddings in grand variable exponent Hajasz-Sobolev spaces are also studied. Some applications to the approximation theory and boundary value problems of analytic functions are presented as well.
The book is aimed at an audience ranging from researchers in operator theory and harmonic analysis to experts in applied mathematics and post graduate students. In particular, we hope that this book will serve as a source of inspiration for researchers in abstract harmonic analysis, function spaces, PDEs and boundary value problems.
18. Integral Operators on Weighted Grand Lebesgue Spaces (WGLS).-
19. Integral Operators in Grand Mixed-Normed Function Spaces.- 20. Grand
Variable Exponent Function Spaces.- 21. Extrapolation in Grand Function
Spaces.- 22. Grand Variable Haj laszSobolev and Hölder Spaces.- 23. Grand
Lebesgue Type Spaces.