Format: Hardback, 626 pages, height x width: 235x155 mm, 4 Illustrations, black and white; XVII, 626 p. 4 illus., 1 Hardback
Series: Springer Monographs in Mathematics
Pub. Date: 30-May-2025
ISBN-13: 9783031841194
The book deals with qualitative analysis of the mathematical model of flow of a viscous incompressible fluid around a translating and rotating body. The considered mathematical model, which represents the description of the flow in a coordinate system attached to the body, is derived from the NavierStokes equations by means of an appropriate transformation. The core of the book is the mathematical theory of the transformed equations. Most of the text is devoted to the theory of the linearized versions of these equations (i.e. the Stokes- and Oseen-type equations), because they play a fundamental role in the theory of the complete nonlinear system.
Considering strong, weak, and very weak solutions, we present the L2 and Lq theories and the weighted space theory (with Muckenhaupt's weights) in the whole space and in an exterior domain. The book also contains the spectral analysis of the associated linear Stokes-Oseen-type operators and the information on semigroups generated by these operators, and related resolvent estimates.
Moreover, the book describes the asymptotic behavior of solutions and leading profiles of solutions for linear and as well as nonlinear systems.
Further, the book contains studies of the problem with artificial boundary (important in numerical analysis), an introduction to the theory of the corresponding complete nonlinear system in both steady and nonsteady cases, a brief description of the situation when the rotation is not parallel to the velocity at infinity and necessary estimates of the related Oseen kernels.
Part I Introduction and preliminaries.- 1 Introduction.-
2 Preliminaries.- Part II Linear theory.- 3 The steady Stokes type
problem.- 4 The Steady Oseen type problem.- 5 Representation formula and
asymptotic behavior.- 6 Artificial boundary conditions for Oseen type
problem.- 7 The Oseen-type problem: a weak solution in anisotropical L2
-spaces.- 8 Stokes and Oseentype operators: spectral theory and generated
semigroups.- Part III Navier-Stokes type equations.- 9 The stationary
NavierStokestype problem.- 10 Pointwise decay for the stationary
NavierStokes type problem.- 11 Asymptotic behavior of the solutions of the
NavierStokes type problem.- 12 The nonstationary NavierStokestype
problem.- Part IV Appendix.- 13 Appendix.
Format: Paperback / softback, 302 pages, height x width: 235x155 mm, XIII, 302 p., 1 Paperback / softback
Series: Universitext
Pub. Date: 25-May-2025
ISBN-13: 9783031848339
Algebraic Geometry is a huge area of mathematics which went through several phases: Hilbert's fundamental paper from 1890, sheaves and cohomology introduced by Serre in the 1950s, Grothendieck's theory of schemes in the 1960s and so on. This book covers the basic material known before Serre's introduction of sheaves to the subject with an emphasis on computational methods. In particular, we will use Grobner basis systematically.
The highlights are the Nullstellensatz, Grobner basis, Hilbert's syzygy theorem and the Hilbert function, Bezouts theorem, semi-continuity of the fiber dimension, Bertini's theorem, Cremona resolution of plane curves and parametrization of rational curves.
In the final chapter we discuss the proof of the Riemann-Roch theorem due to Brill and Noether, and give its basic applications.The algorithm to compute the Riemann-Roch space of a divisor on a curve, which has a plane model with only ordinary singularities, use adjoint systems. The proof of the completeness of adjoint systems becomes much more transparent if one use cohomology of coherent sheaves. Instead of giving the original proof of Max Noether, we explain in an appendix how this easily follows from standard facts on cohomology of coherent sheaves.
The book aims at undergraduate students. It could be a course book for a first Algebraic Geometry lecture, and hopefully motivates further studies.
1. Hilberts Nullstellensatz.-
2. The algebra-geometry dictionary.-
3.
Noetherian rings and primary decomposition.-
4. Localization.-
5. Rational
functions and dimension.-
6. Integral ring extensions and Krull dimension.-
7. Constructive ideal and module theory.-
8. Projective algebraic geometry.-
9. Bezouts theorem.-
10. Local rings and power series.-
11. Products and
morphisms of projective varieties.-
12. Resolution of curve singularities.-
13. Families of varieties.-
14. Bertinis theorem and applications.-
15. The
geometric genus of a plane curve.-
16. Riemann-Roch.- A. A glimpse of sheaves
and cohomology.- B. Code for Macaulay2 computation.- References.- Glossary.-
Index.
Format: Hardback, 138 pages, height x width: 240x168 mm, 3 Illustrations, color;
1 Illustrations, black and white; X, 138 p. 4 illus., 3 illus. in color., 1 Hardback
Series: Synthesis Lectures on Mathematics & Statistics
Pub. Date: 15-Jun-2025
ISBN-13: 9783031846465
This book presents algebra in a concise and clear way, allowing beginner students to quickly attain the required proficiency. As to opposed to existing books on the subject that cover too many topics, some of which are too complex and intimidating for a first course in linear algebra, this book only presents the essential topics in a more user-friendly manner. The author includes an optimized order of topics that are adapted to the learning patterns of students. In addition, carefully designed examples are presented to enhance reader confidence to master the material and to avoid frequently observed frustration. This textbook is ideal for a one semester course on basic linear algebra for college students majoring in mathematics, engineering, and other sciences.
Linear Equations.- Matrix Algebra.- Determinants.- Vector Spaces.-
Eigenvalues and Eigenvectors.- Orthogonality.
Format: Hardback, 288 pages, height x width: 235x155 mm, 42 Illustrations, color;
11 Illustrations, black and white; X, 288 p. 53 illus., 42 illus. in color., 1 Hardback
Series: Research Perspectives Ghent Analysis and PDE Center 11
Pub. Date: 08-Jul-2025
ISBN-13: 9783031872129
This volume presents the latest theoretical and experimental advancements in the field of inverse problems in recent years. It includes outstanding research results that reflect current theoretical and numerical aspects of inverse problems and their various applications. The volume is a collection of selected contributions from nearly three hundred invited presentations at the International Conference "Inverse Problems: Modelling and Simulation" (IPMS 2024) held from May 26 to June 1, 2024, in Malta.
The topics covered in this volume are closely related to emerging deterministic and stochastic models in the fields of medical imaging, biology, geophysics, radar, computer science, communication theory, signal processing, visualization, engineering, and economics. The contributions in this volume reflect a broad range of problems in the theory and applications of inverse problems that are useful for mathematicians, physicists, engineers, and researchers working with inverse problems.
- Part I: Detection Methods.-
1. Determination of cavities in nonlinear parabolic systems arising from electrophysiology.-
2. Source detection on a network: numerical considerations.-
3. Resonator-Based Mass Detection in Nanostructures.-
4. Exploring instabilities of inverse problem solvers with low-dimensional manifolds.-
5. The multifrequency topological derivative method as a data processing tool in nondestructive testing.-
6. Motion Detection in Diffraction Tomography.-
Part II: Geometric Inverse Problems.-
7. Survey on Broken Ray Transforms.-
8. Inverse Problems for Twisted Geodesic Flows.-
9. Applications of momentum ray transforms in inverse problems.-
Part III: Inverse and Control Problems in Vibrating Structures.-
10. On the use of a roving harmonic load to locate cracks in shear deformable beam.-
11. Identification of out-of-plane loads over Timoshenko beams.-
12. Inverse Source Problems of Damped Vibrating Beam and Plate Models.- Part IV: Inverse Problems and Imaging.-
13. Higher order autocorrelations.-
14. Inverse Problems in Image Restoration.-
15. A Counterexample to Convergence for Multiscale.-
16. Three-dimensional brassiere design for electrical impedance tomography and numerical conductivity reconstructions in EIDORS.-
17. Permittivity Estimation Using Plasmonics.- Part V: Inverse problems and Regularisation.-
18. On Fourier Phase Retrieval by Differential Intensity Measurements in Finite Dimensions.-
19. Bi-level regularization via iterative mesh refinement for aeroacoustics.-
Part VI: Inverse Problems for Fractional Equations.-
20. The Inverse Problem for the Fractional Conductivity.-
21. Inverse problems for simultaneous determination of source terms and several scalar parameters of fractional diffusion equations.-
22. A local uniqueness theorem for the fractional SchrOodinger equation on closed Riemannian manifolds.-
23. Time-fractional diffusion equations of piecewise constant time-varying order.- Part VII: Inverse Problems for PDEs.-
24. A global optimum-informed greedy algorithm for A-optimal experimental design.-
25. Multi-dimensional operators with Sonine kernels.-
26. Numerical Reconstruction of Orders in Coupled Systems of Subdiffusion Equations.-
27. Inverse problems for a wave equation with an interface.-
28. New derivation of relaxation tensor for anisotropic extended Burgers model.-
29. Inverse Problems for Screens.-
30. Shearlet localization operator and microlocal analysis.-
31. Strong Unique Continuation for the Damped Wave.-
Part VIII: Inverse Scattering Problems.-
32. Reduced Order Lippmann-Schwinger-Lanczos Inverse Scattering Method.-
33. Transparent scatterers and transmission eigenvalues.-
34. On passive inverse obstacle scattering problems with Neumann and Robin boundary conditions.-
35. New series representations and reconstruction techniques in coefficient inverse problems.-
36. A method to extrapolate the data for the inverse magnetisation problem with a planar sample.-
37. Lippmann-Schwinger-Lanczos approach for inverse scattering problem of Schrodinger equation in the resonance frequency domain.-
Part IX: Machine Learning.-
38. Quantum-inspired classification algorithms.-
Part X:Radon Transforms and Applications.-
39. Geometry of domains and algebraic type of their Radon transforms.-
40. Remarks on the Interior Problem for the Radon transform.-
41. Range conditions for some divergent-beam transforms.-
42. Super-resolution reconstruction from truncated Hankel transform.-
Part XI: Stochastic Problems and Bayesian Inversion.-
43. Inverse stochastic variational formulation for a control economic equilibrium problem.-
44. Sampling in Bayesian inversion accelerated by surrogate models.
Format: Hardback, 338 pages, height x width: 235x155 mm, 25 Illustrations, color;
3 Illustrations, black and white; X, 338 p. 28 illus., 25 illus. in color., 1 Hardback
Series: Springer INdAM Series 64
Pub. Date: 29-Jun-2025
ISBN-13: 9789819635832
This present book collects a distinguished selection of contributions by scholars who participated as speakers or as visiting scientists in the intensive programme Puglia Summer Trimester 2023 took place in Bari, Italy, from April to July 2023, and also includes contributions by further scholars who are expert in related fields. The programme was structured around a series of main meetings, including a general conference and a summer school, supplemented by the local presence and activities of an amount of visiting scientists. Additionally, efforts were made to disseminate and popularise mathematics among schools and the general public, with the aim of extending the programme's impact beyond the immediate academic sphere. Each chapter, in the form of retrospective reviews, overviews on recent developments, announcements and comments of new results, as well as outlooks on future perspectives, represents some of the main scientific instances of the trimester in Bari. The trimester was actually focussed on a spectrum of mathematical problems, directly stemming or inspired from a variety of physical domains, involving singular modelling, asymptotic and emergent phenomena, singular interactions, non-trivial limit effects. Natural backgrounds are quantum physics, cold atom physics, soft matter physics, with methods and tools, suitably adapted to such singular settings, spanning across operator and spectral theory, functional analysis, probability, differential geometry, partial differential equations, and numerical analysis.
Globally integrable quantum systems and their perturbations.- On
two-dimensional Dirac operators with $\delta$-shell interactions supported on
unbounded curves with straight ends.- Attractor Subspace and Decoherence-Free
Algebra of Quantum Dynamics.- Algebraic localization of generalized Wannier
bases implies Roe triviality in any dimension.- Hearing the boundary
conditions of the one-dimensional Dirac operator Bosonized Momentum
Distribution of a Fermi Gas via Friedrichs Diagrams.- Self-adjointness and
Domain of Generalized SpinBoson Models with Mild Ultraviolet Divergences.-
Random Linear Systems with Quadratic Constraints: from Random Matrix Theory
to replicas and back.- New analytical and geometrical aspects on
Trudinger-Moser type inequality in 2D.- Resolvent limits of exterior boundary
value problems and singular perturbation of Laplace operator in 3D.- The
Search for NLS Ground States on a hybrid domain: motivations, methods, and
results.- From microscopic to macroscopic: the large number dynamics of
agents and cells, possibly interacting with a chemical background.- Open
problems and perspectives on solving Friedrichs systems by Krylov
approximation.- Singularity: a Seventh Memo.
Format: Hardback, 630 pages, height x width: 235x155 mm, 84 Illustrations, black and white; X, 630 p. 84 illus., 1 Hardback
Series: Grundlehren der mathematischen Wissenschaften 363
Pub. Date: 13-Jun-2025
ISBN-13: 9783031848445
This book is the second volume of a work on complex analytic cycles and the results, stated without proof in the first volume, are proved here. It begins with the construction of the reduced complex space formed by all compact cycles of a given complex space. Following this construction the main subjects of the book are:
Fundamental class of a cycle and relative fundamental class of an analytic family of cycles
Intersection theory with parameters on complex manifolds and more generally on nearly smooth complex spaces
Holomorphic currents on reduced complex spaces
Chow varieties and cycle spaces of quasi-projective complex spaces
Natural morphism from the Douady space to the cycle space
Holomorphic convexity in cycle spaces and integration of $\bar{partial}$-cohomology classes on cycles
Strong Kahlerianity of cycle spaces of Kahler manifolds
Numerous important applications of cycle space theory
Preliminaries needed in the book in addition to the material of the first volume, for instance sheaf cohomology with support, are explained in detail, making this two-volume work quite self-contained. The French version of the present book was published in 2020 by the French Mathematical Society in the series Cours Specialises and during the translation process the authors have in many ways improved the original version.
5 Construction of the Cycle Space.-
6 Relative fundamental classes.-
7 Intersection theory.-
8 Holomorphic currents and Intersection Theory in a nearly smooth complex spaces.-
9 Chow varieties and Cycle spaces.-
10 Douady > Cycles.-
11 Convexity of Cycles space.-
12 Kahlerianity of Cycle Spaces.
Format: Hardback, 275 pages, height x width: 235x155 mm, 109 Illustrations, color; 28 Illustrations,
black and white; XVI, 275 p. 137 illus., 109 illus. in color., 1 Hardback
Series: Springer Proceedings in Mathematics & Statistics 482
Pub. Date: 01-Jul-2025
ISBN-13: 9789819634590
This volume presents a curated selection of papers presented at the International Conference on Applied and Industrial Mathematics (ICAIM 2023), hosted by Sharda University in Greater Noida, Uttar Pradesh, India, from 24-26 March 2023. It delves into diverse realms of mathematical modelling, applied analyses, computational methods and industrial mathematics. Each chapter within this collection offers intriguing insights into tackling real-world challenges through the lens of mathematical modelling and computational approaches. The book traverses an array of compelling subjects from safeguarding secrets through specialized codes to optimizing solar energy utilization. It illuminates how mathematics is potent in unravelling intricate problems, such as understanding disease propagation or enhancing machine learning algorithms. Through lucid explanations and engaging examples, this volume is tailored for curious minds eager to delve into the marvels of mathematics from fresh perspectives.
M. Yunusovna Rasulova, A new method of cryptography providing perfect
confidentiality of information.- B. ler, U. ener, A. Tokgozlu, Z. Aslan,
P. Baumann, Prediction of solar energy potential with machine learning and
deep learning models.- S. Doven, Z. Aslan, Total Electron Content and Wavelet
Transformation Analysis: Understanding the Role of Modelling.- Muhammad S.
Jahan, A. Sharmin, B. M. Walters, T. C. Crosby, Free Radical, Antioxidant and
Human health.- M. Premkumar, P. Shirley Muller, Maheswari, J. Jeyapackiam,
Prasanna, Prakash, Salim Al Hudafi, Algebraic Properties of Doubt - Fuzzy
CI-Sub Algebras and Ideals in CI-Algebra.- R. Sharma, V. Ghlawat, K. Alam,
Elastoplastic behavior of transversely isotropic piezoelectric disc made of
functionally graded material with variable thickness under rotation.- R.
Chanian, H D Arora, Detection and classification of pneumonia from chest
x-rays using image based deep learning methods.- Y. Aakriti Kumari, Y. Negi,
S. Varshney, Precision agriculture using IoT sensors.- N. G. Tiwari, S.
Kumar, A. Routray, On the analysis of a Very Severe Cyclonic Storm Nilofar
over the Arabian Sea: A numerical weather prediction model study.- P. Gupta,
S. Gupta, S. Srivastav, Crypto-encoding communication with graph theory.-
Mangani D. Kazembe, Sudeep Varshney, Keshav Gupta, Cybersecurity incidents in
relation to fraudulent SIM card registration in Malawi.- G. Gupta, N. Kumar,
P. Tripathi, P. Agarwal, I. Haider, Supply Chain Analysis and Prediction
using Machine Learning.- M. Shamsi, F. Marvasti, Optimal Transport: A
Promising Technique for Causal Inference Applications.- R. Khurana, M.
Sharma, S. Singh, A. Singh, Analysis of a Queueing model with Catastrophe and
First Exceptional Service.- R. Kumar, A. Anand, N. Singh, S. Ramamoorthy, M.
Alam, CNN-based Mathematical Model for Sub-Classification of Non-Small Cell
Lung Cancer into Squamous Cell Carcinoma and Adenocarcinoma.- G. Luugering,
Friction dominated flow in gas-networks: modeling, simulation, optimal
Control and domain decompositions.