Format: Paperback / softback, 263 pages, height x width: 235x155 mm, 1 Illustrations, color;
3 Illustrations, black and white; XIV, 263 p. 4 illus., 1 illus. in color.,
Series: La Matematica per il 3+2 171
Pub. Date: 30-Apr-2025
ISBN-13: 9783031851445
This book provides an accessible introduction to the theory of L-functions, emphasising their central role in number theory and their direct applications to key results. Designed to be elementary, it offers readers a clear pathway into the subject, starting from minimal background. It describes several important classes of L-functions Riemann and Dedekind zeta functions, Dirichlet L-functions, and Hecke L-functions (for characters with finite image) by showing how they are all special cases of the construction, due to Artin, of the L-function of a Galois representation. The analytic properties of abelian L-functions are presented in detail, including the full content of Tate's thesis, which establishes analytic continuation and functional equations via harmonic analysis. General Hecke L-functions are also discussed, using the modern perspective of id?les and ad?les to connect their analytic theory with the representation-theoretic approach of Artin's L-functions. A distinguishing feature of this book is its accessibility: while largely avoiding arithmetic geometry, it provides introductions to both algebraic number theory and key aspects of representation theory. This approach ensures that the material is accessible to both beginning graduate students and advanced undergraduates. Applications play a central role throughout, highlighting how L-functions underpin significant results in number theory. The book provides complete proofs of the prime number theorem, Dirichlet's theorem on primes in arithmetic progressions, Chebotarev's density theorem, and the analytic class number formula, demonstrating the power of the theory in solving classical problems. It serves as an ideal introduction for advanced undergraduates and beginning graduate students and can also be a useful reference for preparing a course on the subject.
- Part I Classical ??-functions and applications.-
1. What is an ??-function?.-
2. The Prime Number Theorem.-
3. Review of Algebraic Number Theory.-
4. A Primer of Representation Theory.-
5. The ??-Function of a Complex Galois Representation.-
6. Dirichlets Theorem on Arithmetic Progressions.-
7. The Chebotarev Density Theorem.-
Part II Prerequisites for Tates Thesis.-
8. The Haar Measure.-
9. Abstract Fourier Analysis.-
10. Review of Local Fields.-
11. Restricted Direct Products.-
Part III Tates Thesis.-
12. The Local Theory.-
13. The Global Theory.-
14. Hecke ??-Functions.-
15. Recovering the Classical Theory.-
16. An Extended Example: the ??-Function of a CM Elliptic Curve.
Format: Hardback, 226 pages, height x width: 235x155 mm, 61 Illustrations, color;
6 Illustrations, black and white; X, 226 p. 67 illus., 61 illus. in color.,
Series: Springer Proceedings in Mathematics & Statistics 487
Pub. Date: 19-May-2025
ISBN-13: 9789819625789
This book contains select chapters of proceedings presented at the 6th International Conference on Frontiers in Industrial and Applied Mathematics (FIAM-2023), held at the Birla Institute of Technology and Science, Pilani-Dubai Campus, UAE, on 2122 December 2023. It deals with mathematical theory and its applications to the various disciplines of engineering and sciences. The book illustrates the mathematical simulation of scientific problems and cutting-edge development in multiple branches of mathematics, including various computational and modeling techniques with case studies and concrete examples. The book is useful to graduate students, research scholars and professionals who are interested in the real applications of mathematics in the areas of computational and theoretical fluid dynamics, server queues, Lie group theory, fixed point theory, image processing, biomathematics, nonlinear dynamics and approximation theory.
A. R. Nieto, Jesus M. Seoane, and Miguel A. F. Sanjuan, Exploring Noisy
Chaotic Hamiltonian Systems.- D. Parmar, B.V. Rathish Kumar, S.V.S.S.N.V.G
Krishna Murthy, Numerical study of time-fractional derivative on double
diffusive convective flow of nanofluid in a wavy porous cavity.- C. Deniz
Canal and A. C. Benim, Numerical Study of Co-firing in Swirl Burner using
Coal- Biomass Blends.- A. Bisht, R. Sharma, Heat Transfer in Tangent
Hyperbolic Nanofluid Flow over a Stretching Sheet with Convective Boundary.-
A. A. Miloua, Results of asymptotic analysis of an elliptic equation.- S. K.
Srivastavaa and S. Devaiyab, Uniform approximation of functions g L[ 0,
)-space using Eq.T -means of its Fourier-Laguerreseries.- S. Mulchan, S. Rao
Gunakala, The Lie Group Analysis of the 2D Time Independent Isotropic
Harmonic Oscillator.- L. Mohan and A. Prakash, Analysis and simulation of
fractional Convection- Diffusion model with Caputo derivative.- L. Wangwe and
S. Kumar, Common Fixed Point Theorem for Multivalued Mappings in Weak-Partial
b- Metric Space with an Application.- S. Kumar and S. V. S. S. N. V. G.
Krishna Murthy, B. V. Rathish Kumar, Deep learning based parametric
estimation in double-diffusive convective flow.- Kailash C. Madan, On a
??[ ??]/??/1 Queue with Two Types of Random Failures,
Delay in Starting the Major Repairs and Reneging During the Down Time.- V.
Khaladkar and M. Kumar, Triple secure encryption scheme 3-channel image based
on Hankel transform, geometric transforms and hyper chaotic maps.- C. Deniz
Canal, M. Diederich, O. Karacay, A. C. Benim, Investigation of Boiler
Efficiency Improvements via Enthalpy Wheel with Application to a Biomass
Boiler.- V. H. Vatsal, B. Kumar Jha and T. Pal Singh, To Study the Effect of
ER Flux and Orai Flux on Fractional Calcium Diffusion in Neuronal Disorder.-
S. Maheshwari and R. Sharma, Numerical Study of Thermo-Convective Instability
of Au-Fe3O4 Hybrid Bi-Viscous Bingham Nanofluid.
Format: Hardback, 342 pages, height x width: 235x155 mm, 60 Illustrations,
color; 3 Illustrations, black and white; VIII, 342 p. 63 illus., 60 illus. in color.
Series: Springer Proceedings in Mathematics & Statistics 490
Pub. Date: 07-May-2025
ISBN-13: 9783031841507
This proceedings volume compiles papers presented at the 5th International Conference on Mathematics and its Applications in Science and Engineering ICMASE 2024, held on September 1618, 2024, by the Polytechnic Institute of Coimbra, Portugal. The ICMASE 2024 was a hybrid conference, featuring both in-person and virtual attendance.
The works in this volume explore recent developments in the application of mathematics to science and engineering, focusing on mathematical and computational modeling of real-world problems. Topics include algebra and number theory, analysis, geometry, statistics, computational and discrete mathematics, as well as their intersections with engineering applications. Additionally, educational aspects of mathematics in engineering fields are addressed.
This volume is intended for researchers, practitioners, and graduate students, particularly those interested in advanced methods for applying mathematics across various contexts and fields.
Distributed Fusion Estimation in the Presence of Measurement
Quantization and Mixed Attacks.- p-Frobenius Numbers of Numerical Semigroups
Generated by Three Consecutive Squares.- On Solutions of a Third Order Linear
Difference Equation with Variable Coefficients Applications.- Binet-Fibonacci
Calculus and N = 2 Supersymmetric Golden Quantum Oscillator.- Geometry and
Entanglement of Super-Qubit Quantum States.- On the Bi-periodic Edouard and
the Bi-periodic EdouardLucas Numbers.- The Investment Portfolio Selection
with Social Network Decision-Making with Minimum Cost Consensus Model and
Incomplete Fermatean Fuzzy Preference Relations.- Boundary Value Problems for
the Bitsadze Equation on a Quarter Plane.- Galois Bundles and Automorphisms
of the Principal Bundle Moduli Space.- Linear Algebra in Crystal Geometry,
and Vice Versa.- On Dual Biquaternionic Sequence Involving Vietoris
Numbers.- A Quadratic Programming Model for Operating Rooms Scheduling based
on Resources Availability.- Derivative method for solving cubic equations.-
Improved Computational Techniques for Heat Sources Localization.- Open access
fisheries model considering depensatory growth functions in the exploited
resource.- An Empirical Comparison of Supervised Machine Learning Models in
Predicting Mathematics Performance in Somaliland.- Using SOLO Taxonomy to
develop a structured design for mathematics exam questions.- Application of
Supervised Machine Learning Algorithms to Identify the Prevalence and
Determinants of Spontaneous Abortion among Ever-married Women in Somaliland:
Insights from SLDHS Data 2020.- Modified Hungarian Method (MHM) in Optimizing
Competency-Preference Scores in Lecturer-To-Course Assignment.- Effects of
autonomous vehicles on particulate matter emissions.- Codimension-2
Bifurcation Analysis of a Modied Non-degenerate Fisher Equation Introducing
Two Unfolding Parameters.- Modelling Medfly Pest Management.- BETWEEN
-CLOSED AND IG-CLOSED SETS.- Fault Injection Attacks against RSA-CRT
Digital Signature.- Analysis of Prognostic Factors in Prostate Cancer - A New
Approach.- On k-order Jacobsthal Polynomials and Their Properties.- On
Euclidean Norms Of Max On Euclidean Norms Of Max Matrices With Chebyshev
Polynomials.- Bridging academic learning and community service.- Escape Rooms
and Students Competencies.- Descriptive and Inferential Analysis of Renal
Health and Patterns of Water Consumption: A case study of Ciudad Hidalgo.-
Modeling Solar Energy Through Mathematics.- Problem-Based Learning, Teamwork
and Entrepreneurship in the Numerical Methods Course.- Advanced Teaching
Strategies for Enhancing STEM Education in Higher Institutions.- Numerical
Methods: Artifacts in teaching in a mathematics degree.
Format: Hardback, 274 pages, height x width: 235x155 mm, 91 Illustrations, black and white; X, 274 p. 91 illus.,
Series: Springer Proceedings in Mathematics & Statistics 491
Pub. Date: 28-Apr-2025
ISBN-13: 9789819630974
This volume contains selected chapters on topics presented at the International Conference on Modeling, Analysis and Simulations of Multiscale Transport Phenomena (ICMASMTP 2022), held at the Department of Mathematics, Indian Institute of Technology Kharagpur, West Bengal, India, from 2225 August 2022. It contains chapters on applications of FLOW THROUGH POROUS MEDIA, diffusionreaction equations, fluid dynamics, multi-scale analysis, electrokinetic transport processes, microfluidics modelling, numerical analysis, and related topics. Contributors are academicians, experts and researchers in various disciplines of applied mathematics, numerical analysis and scientific computation, having applications in physics, engineering, chemistry, biology and medical science.
A. Jungel and M. Biswas, Global Martingale Solutions to a Segregation
Cross-diffusion System with Stochastic Forcing.- A. Sandhya, M. Siva Mala, R.
Sandhya and G.Venkata Ramana Reddy, MHD Casson Fluid Flow over a Vertical
Porous Surface with the Effects of Radiation and Chemical Reaction.- S.
Singh, B. Sagar and S. Saha Ray, PaulPainleve Approach to Solve (3 +
1)-dimensional Extended Sakovich Equation Arising in Fluid Dynamics.- H.
Ohshima, Unsteady Electrophoresis of a Spherical Colloidal Particle:
Time-dependent Transient Henry Function.- H. Kumar Shaw, Mallika Aich and
Subhamoy Singha Roy, Reverse Transcription Polymerase Spin Chain Reaction.-
A. K. Nayak and M. Majhi, Numerical Study of Ion Transport and Convective Min
Micro Channel with Nozzle/Diffuser.- M. Chaudhary and H. Shankar Mahato,
Analytical Solution of Multi-species Pollutant Transport Problem Coupled with
Linear Reactions and Additional Source/Sink Term.- N. Kumar, S. Kumar, V.
Kumar, S. Datta and S. S. Roy, A Theoretical Model Slant to the Fermi Energy
for Low-dimensional Materials.- P. Mondal and D. K. Maiti, A Mixed Convection
Two-dimensional Flow and Heat Transfer of Power Law Fluid Past through Porous
Microchannel.- P. Koner and S. Bera, Electroosmotic Flow of Generalized
Maxwell Fluids in Polyelectrolyte Grafted Nanopore Modulated by Ion
Partitioning Effects under AC Electric Field.- R. Bhardwaj and Inderjeet,
Numerical Simulation of Parabolic Partial Differential Equation.- N. Chauhan,
FVM Simulation Study for Dispersion Pattern of Indoor Thoron Gas using
Computational Fluid Dynamics (CFD) Modeling: Effect of Room Configuration.-
S. Singh and S. Saha Ray, Propagation of Two-wave Solitons Depending on
Phase-velocity Parameters of Two Higher-dimensional Dual-mode Models in
Nonlinear Physics.- S. S. Banerjee, A. Bhattacharyya, S. K. Sharma and S. C.
Panja, Delay Modelling of Selected Trains in Indian Railways.- S. Behera,
Analytical Solutions of Fractional Order NewellWhiteheadSegel Equation.- S.
S. Barman and S. Bhattacharyya, Gel Electrophoresis of a Polarizable Charged
Colloid with Hydrophobic Surface.- S. Ghosh and S. S. Roy, Photon Echo on DNA
Molecules: A Theoretical Study.- S. Hossain, K. Ghoshal and A. Dhar,
Numerical Simulation of a Simplified Stratification Model of Suspended
Sediment Concentration in an Open-channel Turbulent Flow.- S. Sen, S. Hossain
and K. Ghoshal, Effects of Hydrodynamic Phenomena on Two-dimensional
Distribution of Suspended Sediment Concentration in an Open Channel Flow.- Y.
Nandkuliyar and S. S. Roy, Theoretical Models of DNA Elasticity.
Format: Paperback 276 pages, height x width: 235x155 mm, 3 Illustrations,
color; 7 Illustrations, black and white; X, 276 p. 10 illus., 3 illus. in color.,
Series: Ecole d'Ete de Probabilites de Saint-Flour 2364
Pub. Date: 09-May-2025
ISBN-13: 9783031851599
This monograph aims to offer a concise introduction to optimal transport, quickly transitioning to its applications in statistics and machine learning. It is primarily tailored for students and researchers in these fields, yet it remains accessible to a broader audience of applied mathematicians and computer scientists. Each chapter is complemented with exercises for the reader to test their understanding. As such, this monograph is suitable for a graduate course on the topic of statistical optimal transport.
1. Optimal Transport.-
2. Estimation of Wasserstein distances.-
3. Estimation of transport maps.-
4. Entropic optimal transport.-
5. Wasserstein gradient flows: theory.-
6. Wasserstein gradient flows: applications.-
7. Metric geometry of the Wasserstein space.-
8. Wasserstein barycenters.
Format: Paperback 150 pages, height x width: 235x155 mm, 5 Illustrations, black and white; X, 150 p. 5 illus.,
Series: Lecture Notes in Mathematics 2372
Pub. Date: 06-May-2025
ISBN-13: 9783031866630
This book provides a new approach to traces, which are viewed as linear continuous functionals on some function space. A key role in the analysis is played by integrals related to finitely additive measures, which have not previously been considered in the literature. This leads to Gauss-Green formulas on arbitrary Borel sets for vector fields having divergence measure as well as for Sobolev and BV functions. The integrals used do not require trace functions or normal fields on the boundary and they can deal with inner boundaries. For the treatment of apparently intractable degenerate cases a second boundary integral is used. The calculus developed here also allows integral representations for the precise representative of an integrable function and for the usual boundary trace of Sobolev or BV functions. The theory presented gives a new perspective on traces for beginners as well as experts interested in partial differential equations. The integral calculus might also be a stimulating tool for geometric measure theory.
1. Introduction.-
2. Preliminaries About Measures.-
3. Theory of Traces.-
4. Divergence Theorems.
Format: Paperback / softback, 205 pages, height x width: 240x168 mm,
35 Illustrations, color; 13 Illustrations, black and white; X, 205 p. 48 illus., 35 illus. in color.ck
Series: Frontiers in Mathematics
Pub. Date: 19-May-2025
ISBN-13: 9783031857539
This monograph examines a variety of iterative methods in Banach spaces with a focus on those obtained from the Newton method. Together with the authors previous two volumes on the topic of the Newton method in Banach spaces, this third volume significantly extends Kantorovich's initial theory. It accomplishes this by emphasizing the influence of the convexity of the function involved, showing how improved iterative methods can be obtained that build upon those introduced in the previous two volumes. Each chapter presents theoretical results and illustrates them with applications to nonlinear equations, including scalar equations, integral equations, boundary value problems, and more. Convexity in Newton's Method will appeal to researchers interested in the theory of the Newton method as well as other iterative methods in Banach spaces.
The degree of logarithmic convexity.- The Newton method and convexity.-
Accelerations of the Newton method.- Newton-like methods with high order of
convergence.- Optimization of the Chebyshev method.