Format: Hardback, 303 pages, height x width: 235x155 mm, Approx. 315 p.
Series: Problem Books in Mathematics
Pub. Date: 05-Jun-2024
ISBN-13: 9783031564260
The book contains a collection of more than 800 problems from all main chapters of functional analysis, with theoretical background and solutions. It is mostly intended for undergraduate students who are starting to study the course of functional analysis. The book will also be useful for graduate and post- graduate students and researchers who wish to refresh their knowledge and deepen their understanding of the subject, as well as for teachers of functional analysis and related disciplines. It can be used for independent study as well. It is assumed that the reader has mastered standard courses of calculus and measure theory and has basic knowledge of linear algebra, analytic geometry, and differential equations.
This collection of problems can help students of different levels of training and different areas of specialization to learn how to solve problems in functional analysis. Each chapter of the book has similar structure and consists of the following sections: Theoretical Background, Examples of Problems with Solutions, and Problems to Solve. The book contains theoretical preliminaries to ensure that the reader understands the statements of problems and is able to successfully solve them. Then examples of typical problems with detailed solutions are included, and this is relevant not only for those students who have significant difficulties in studying this subject, but also for other students who due to various circumstances could be deprived of communication with a teacher. There are problems for independent solving, and the corresponding selection of problems reflects all the main plot lines that relate to a given topic.
The number of problems is sufficient both for a teacher to give practical lessons, to set homework, to prepare tasks for various forms of control, and for those students who want to study the discipline more deeply. Problems of a computational nature are provided with answers, while theoretical problems, the solutions ofwhich require non-trivial ideas or new techniques, are provided with detailed hints or solutions to introduce the reader to the corresponding ideas or techniques.
Preface.- Banach Spaces.- Hilbert Spaces.- Continuous Linear Functionals.- Hahn - Banach Theorem.- Weak and Weak* Convergence.- Bounded Linear Operators.- Uniform, Strong and Weak Operator Convergences.- Inverse Operators.- Classes of Linear Operators in Hilbert Space.- Compact Sets and Operators.- Spectrum of Linear Operators.- Spectral Theory of Compact Operators.- Integral Equations.- Generalized Functions.- Answers, hints and solutions.- List of notations.- References.
Format: Hardback, 180 pages, height x width: 235x155 mm, XX, 180 p.,
Series: Lecture Notes in Morphogenesis
Pub. Date: 29-Jul-2024
ISBN-13: 9783031549816
The body of work presented in this book comes from research carried out since 2017 as part of the international "Actualite de Rene Thom" project. This project was initially entitled "Morphology and qualitative dynamics: Knowledge of forms / Forms of knowledge". Subsequently, the name "Relevance of Rene Thom" was chosen for its clarity and evocative power.
The aim of this research project is to promote the scientific relevance of Rene Thom's thinking on forms, and to demonstrate the importance of his method and discoveries. It is based on discussions of Thom's thinking and the method he proposes - i.e., to seek out dynamic structures in order to understand changes of form in nature and at the human-social level, to explain the transformation of these dynamic forms, to study the morphologies of process in various fields in order to advance scientific knowledge...
The relevance of this thinker has manifested itself in the form of monthly sessions of a research seminar, held from 2017 to 2022, as well as in the form of international congresses (2018, 2019), bringing together the greatest friends and continuators, both of the work of Rene Thom himself, and of reflection on morphogenetic dynamics in the most diverse disciplines. This created a space for dialogue and listening between the exact sciences and the social and human sciences. Indeed, the fields of study are necessarily interdisciplinary, since, as Rene Thom teaches us, morphological organization, or form, in its exchanges with matter, must be considered as "independent" of its substrate, i.e. the environment in which this morphogenesis unfolds.
Finally, this book marks a symbolic moment: it takes shape in the year that marks the centenary of the birth of Rene Thom, who was born in the French town of Montbeliard in 1923. To mark this centenary (1923-2023), a number of initiatives have been launched to celebrate the discoveries and advances of this mathematician-philosopher, ashe liked to call himself The publication of the present book is one more, which we hope will shed light that will stimulate the morphological gaze Thom so urged us to adopt.
Rene Thom between Philosophy and Semiotics.- Rene Thom between Geography
and Urbanism.- Rene Thom between Psychology and Biology.- Rene Thom, a
personal Testimony
Format: Hardback, 240 pages, height x width: 235x155 mm, 1 Illustrations, color;
1 Illustrations, black and white; X, 240 p. 2 illus., 1 illus. in color.
Series: Springer INdAM Series 56
Pub. Date: 16-Jun-2024
ISBN-13: 9789819702244
Kolmogorov equations are a fundamental bridge between the theory of partial differential equations and that of stochastic differential equations that arise in several research fields.
This volume collects a selection of the talks given at the Cortona meeting by experts in both fields, who presented the most recent developments of the theory. Particular emphasis has been given to degenerate partial differential equations, It? processes, applications to kinetic theory and to finance.
Chapter 1. Local Regularity for the Landau Equation (with Coulomb Interaction Potential).
Chapter 2. L 2 Hypocoercivity methods for kinetic Fokker-Planck equations with factorised Gibbs states.
Chapter 3. New Perspectives on recent trends for Kolmogorov operators.
Chapter 4. Schauder estimates for Kolmogorov-Fokker-Planck operators with coefficients measurable in time and Holder continuous in space.-
Chapter 5. A new proof of the geometric Soboleva embedding for generalised Kolmogorov operators.-
Chapter 6. Intrinsic Taylor formula for non-homogeneous Kolmogorov-type Lie groups.
Chapter 7. Form-boundedness and sdes with singular drift.
Chapter 8. About the regularity of degenerate non-local Kolmogorov operators under diffusive perturbations.
Chapter 9. Integration by parts formula for exit times of one dimensional diffusions.
Chapter 10. On averaged control and iteration improvement for a class of multidimensional ergodicdiffusions.
Format: Hardback, 351 pages, height x width: 235x155 mm, 22 Illustrations, color; 64 Illustrations, black and white; XX, 300 p.
Series: Fields Institute Communications 89
Pub. Date: 11-Jun-2024
ISBN-13: 9783031572036
This book explores toric topology, polyhedral products and related mathematics from a wide range of perspectives, collectively giving an overview of the potential of the areas while contributing original research to drive the subject forward in interesting new directions. Contributions to this volume were written in connection to the thematic program Toric Topology and Polyhedral Products held at the Fields Institute from January-June 2020. 16 original conributions were inspired or influenced by the program.
Toric Topology arose as a subject in its own right about twenty-five years ago. It sits at the intersection of commutative algebra, topology, combinatorics, algebraic geometry, and symplectic and convex geometry. Polyhedral products are a functorial generalization of a construction that is at the centre of Toric Topology. They are of independent interest and unify several constructions that arise in a diverse range of areas, such as geometric group theory, homotopy theory, algebraic combinatorics and subspace arrangements.
Preface.- Connected sums of sphere products and minimally non-Golod
complexes.- Toric manifolds over 3-polytopes.- Symmetric products and a
Cartan-type formula for polyhedral products.- Multiparameter persistent
homology via generalized Morse theory.- Compact torus action on the complex
Grassmann manifolds.- On the enumeration of Fano Bott manifolds.- Dga models
for moment-angle complexes.- Duality in toric topology.- Bundles over
connected sums.- The SO(4) Verlinde formula using real polarizations.- GKM
graph locally modelled by TnxS1-action on T*Cn and its graph equivariant
cohomology.- On the genera of moment-angle manifolds associated to
dual-neighborly polytopes: combinatorial formulas and sequences.-
Homeomorphic model for the polyhedral smash product of disks and spheres.-
Invariance of polarization induced by symplectomorphisms.- Polyhedral
products for wheel graphs and their generalizations.- On the cohomology ring
of real moment-angle complexes.
*
Format: Hardback, 410 pages, height x width: 235x155 mm, 24 Illustrations, black and white; XVI, 390 p. 25 illus.
Series: Graduate Texts in Mathematics 302
Pub. Date: 26-Jun-2024
ISBN-13: 9783031564994
This self-contained text introduces Euclidean Fourier Analysis to graduate students who have completed courses in Real Analysis and Complex Variables. It provides sufficient content for a two course sequence in Fourier Analysis or Harmonic Analysis at the graduate level. In true pedagogical spirit, each chapter presents a valuable selection of exercises with targeted hints that will assist the reader in the development of research skills. Proofs are presented with care and attention to detail. Examples are provided to enrich understanding and improve overall comprehension of the material. Carefully drawn illustrations build intuition in the proofs. Appendices contain background material for those that need to review key concepts.
Compared with the authorfs other GTM volumes (Classical Fourier Analysis and Modern Fourier Analysis), this text offers a more classroom-friendly approach as it contains shorter sections, more refined proofs, and a wider range of exercises. Topics include the Fourier Transform, Multipliers, Singular Integrals, Littlewood?Paley Theory, BMO, Hardy Spaces, and Weighted Estimates, and can be easily covered within two semesters.
1 Introductory Material.-
2 Fourier Transforms, Tempered Distributions,Approximate Identities.-
3 Singular Integrals.-
4 Vector-Valued Singular Integrals and LittlewoodPaley Theory.-
5 Fractional Integrability or Differentiability and Multiplier Theorems.-
6 Bounded Mean Oscillation.-
7 Hardy Spaces.-
8 Weighted Inequalities.-
Historical Notes.-
Appendix A Orthogonal Matrices.-
Appendix B Subharmonic Functions.-
Appendix C Poisson Kernel on the Unit Strip.-
Appendix D Density for Subadditive Operators.-
Appendix E Transposes and Adjoints of Linear Operators.-
Appendix F Faa di Bruno Formula.- Appendix G Besicovitch Covering Lemma.- Glossary.-
References.- Index.
Format: Hardback, 743 pages, height x width: 235x155 mm, XVII, 736 p. 15 illus., 1 illus. in color.
Series: Progress in Mathematics 354
Pub. Date: 25-May-2024
ISBN-13: 9783031581199
This monograph introduces readers to locally conformally Kahler (LCK) geometry and provides an extensive overview of the most current results. A rapidly developing area in complex geometry dealing with non-Kahler manifolds, LCK geometry has strong links to many other areas of mathematics, including algebraic geometry, topology, and complex analysis. The authors emphasize these connections to create a unified and rigorous treatment of the subject suitable for both students and researchers.
Part I builds the necessary foundations for those approaching LCK geometry for the first time with full, mostly self-contained proofs and also covers material often omitted from textbooks, such as contact and Sasakian geometry, orbifolds, Ehresmann connections, and foliation theory. More advanced topics are then treated in Part II, including non-Kahler elliptic surfaces, cohomology of holomorphic vector bundles on Hopf manifolds, Kuranishi and Teichmuller spaces for LCK manifolds with potential, and harmonic forms on Sasakian and Vaisman manifolds. Each chapter in Parts I and II begins with motivation and historic context for the topics explored and includes numerous exercises for further exploration of important topics.
Part III surveys the current research on LCK geometry, describing advances on topics such as automorphism groups on LCK manifolds, twisted Hamiltonian actions and LCK reduction, Einstein-Weyl manifolds and the Futaki invariant, and LCK geometry on nilmanifolds and on solvmanifolds. New proofs of many results are given using the methods developed earlier in the text. The text then concludes with a chapter that gathers over 100 open problems, with context and remarks provided where possible, to inspire future research.
Introduction.- Part I: Lectures in locally conformally Kahler geometry.-
Kahler manifolds.- Connections in vector bundles and the Froebenius theorem.-
Locally conformally Kahler manifolds.- Hodge theory on complex manifolds and
Vaisman's theorem.- Holomorphic vector bundles.- CR, Contact and Sasakian
manifolds.- Vaisman manifolds.- The structure of compact Vaisman manifolds.-
Orbifolds.- Quasi-regular foliations.- Regular and quasi-regular Vaisman
manifolds.- LCK manifolds with potential.- Embedding LCK manifolds with
potential in Hopf manifolds.- Logarithms and algebraic cones.- Pseudoconvex
shells and LCK metrics on Hopf manifolds.- Embedding theorem for Vaisman
manifolds.- Non-linear Hopf manifolds.- Morse-Novikov and Bott-Chern
cohomology of LCK manifolds.- Existence of positive potentials.- Holomorphic
S^1 actions on LCK manifolds.- Sasakian submanifolds in algebraic cones.-
Oeljeklaus-Toma manifolds.- Appendices.- Part II: Advanced LCK geometry.-
Non-Kahler elliptic surfaces.- Kodaira classification for non-Kahler complex
surfaces.- Cohomology of holomorphic bundles on Hopf manifolds.- Mall bundles
and flat connections on Hopf manifolds.- Kuranishi and Teichmuller spaces for
LCK manifolds with potential.- The set of Lee classes on LCK manifolds with
potential.- Harmonic forms on Sasakian and Vaisman manifolds.- Dolbeault
cohomology of LCK manifolds with potential.- Calabi-Yau theorem for Vaisman
manifolds.- Holomorphic tensor fields on LCK manifolds with potential.- Part
III: Topics in locally conformally Kahler geometry.- Twisted Hamiltonian
actions and LCK reduction.- Elliptic curves on Vaisman manifolds.-
Submersions and bimeromorphic maps of LCK manifolds.- Bott-Chern cohomology
of LCK manifolds with potential.- Hopf surfaces in LCK manifolds with
potential.- Riemannian geometry of LCK manifolds.- Einstein-Weyl manifolds
and the Futaki invariant.- LCK structures on homogeneous manifolds.- LCK
structures on nilmanifolds and solvmanifolds.- Explicit LCK metrics on Inoue
surfaces.- More on Oeljeklaus-Toma manifolds.- Locally conformally parallel
and non-parallel structures.- Open questions.
Format: Hardback, 391 pages, height x width: 235x155 mm, 98 Illustrations, color; 39 Illustrations, black and white; Approx. 400 p.,
Series: Springer Proceedings in Mathematics & Statistics 455
Pub. Date: 10-Jul-2024
ISBN-13: 9789819721351
This book collects selected, peer-reviewed research presented at the 8th International Conference on Mathematics: Pure, Applied, and Computation, held in Lombok, Indonesia, on 30 September 2023. Organised into three partsPart I: Control Systems, Mathematical Simulation and Modeling; Part II: Formal Methods and Data Science; Part III: Graph Theory and Analysisthe book contains 29 peer-reviewed chapters. Ranging from theoretical to applied results, the book addresses the mathematical models for several phenomena such as investment behavior, unmanned surface vehicles and electronic medical records. It also highlights the progress in the use of satisfiability methods and tools to solve puzzle and pencil games. It showcases how mathematics is used to solve real-world problems.
Part 1: Applied Mathematics (Control Systems, Mathematical Simulation, and Modeling).-
H. Margaretha, N. Satyahadi and F. V. Ferdinand, Simulation of Investment Behaviors using Risk-I
nfluenced Utility Models of Health and Wealth.-
R. K. Dewi, I. Magdalena and I. Marcela, Wave Attenuation by a
Combination of Mangroves and Reefball.- R. M. Valerio and I. Magdalena,
Resonance Detection in a Semi-Closed Basin with Constant Height and
Triangular Width.- R. Rahmawati, L. Harsyiah and Z. W. Baskara, Comparison of
Ridge Regression and Principal Component Regression in Overcoming
Multicolinierity of Factors Affecting Poverty in Indonesia.- Ahmadin, J.
Naiborhu, Fatmawati and Windarto, Identification on Class Nonlinear Control
System with Relative Degree Two.- A. F. Khariri, P. K. Intan, Moh.
Hafiyusholeh, A. H. Asyhar and A. Fanani, Implementation of K-Means Particle
Swarm Optimisation for Clustering Football Players in The Top Five European
Football Leagues.- M. Widianto, C. Imron and B. Widodo, A short review of
numerical modelling for photocatalytic degradation in dye systems.- S.
Subchan, H. Purnawan, T. Asfihani and L. R. Amalia, Reference Tracking of
Quadrotor using Modified Nonlinear Model Predictive Control based on
Nonlinear Disturbance Observer.- D. Savitri, M. Jakfar and L. Putri,
Numerical Simulation and Dynamics of Sedimentation Rate with Seagrass Growth
Considering Dredging Factors.- H. Nuha, N. Siswanto and E. Widodo, A Mixed
Integer Nonlinear Programming for Allocation Polyethylene Terephthalate (PET)
Waste Management in Reverse Logistic Network.- A. Zaki Al Muntazhar, D. Ratna
Sulistyaningrum and Subiono, Quantum K-Nearest Neighbors For Object
Recognition.- T. Asfihani, F. N. Sihan Novita Lutfiani, A. Maulana Syafi'I,
Subchan Subchan and A. Hasan, Adaptive Kalman Filter for Automated Actuator
Fault Diagnosis in Unmanned Surface Vehicle.- E. R M Putri, A. Wahyu
Widianto, A. Hakam, V. Ryan Tjahjono and H. Susanto, A moving average genetic
algorithm (MA-GA)for estimating the COVID-19 dynamic based on a stochastic
SIRD model.- A. Hakam, E. R M Putri and L. Mardiyanto, A general solution of
Black-Scholes equations on some Rainbow options.- F. Ardhiansyah, R. W.
Prastianto, M. Murdjito, K. Suastika and S. Nugroho, Dynamic Response of
Floating Crane During Lifting Operation: A Parametric Study.- Part 2:
Computational Mathematics (Formal Methods and Data Science): M. T. Ammar, M.
Arzaki and G. S. Wulandari, Efficient SAT-Based Approach for Solving Juosan
Puzzles.- J. E. Sakti, M. Arzaki and G. S. Wulandari, Modeling Path Puzzles
as SAT Problems and How to Solve Them.- H. Tanabe and M. Kimura, A
trustworthiness scoring model for reviews using a graph structure.- M. Iqbal,
A. Afandy and N. Hidayat, Non-Linear Reward Deep Q Networks for Smooth Action
in A Car Game.- Arthur de Clairval, L. A. Erwin Schuler, M. F. Rellier, M.
Isa Irawan, I. Mukhlash and M. Iqbal, College Student Activity Recognition
from Smartwatch Dataset.- A. Taryana, D. Adzkiya, M. Syifa'ul Mufid, I.
Mukhlash and A. Abate, LTL Model Checking for Verification of Electronic
Medical Record (EMR) Design.- G. I. Permata Sari, Hsing-Kuo Pao, R. C. Hario
Pribadi and M. Iqbal, Multi-Feature Subgraph Fusion with Text Knowledge on
Citation Link Prediction.- I Komang Pande Prajadhita Wibawa Putra, I.
Irhamah, Nur Iriawan and K. Fithriasari, Predicting Poverty Percentage Based
on Satellite Imagery and Point of Interest Using Support Vector Regression
and Random Forest Regression (Case Study of Central Java Province).- M.
Hutapea, G. Wulandari and M. Arzaki, Preliminary Analysis of Isabelle Proof
Assistant in Graph Programming Verification with GP2.- Part 3: Pure
Mathematics (Graph Theory and Analysis): T. Irvan Haryadi, R. Rinurwati, D.
Winda Setyawati, S. Soleha, I. Herisman, K. Baihaqi and S. Sadjidon, Nonlocal
Edge Metric Dimension on Corona Multiproduct Graphs.- N. Ain Supu, I. M.
Alamsyah and E. Suwastika, The Vertex Degree of Relative g-noncommuting Graph
of the Dihedral Groups.- S. Wibowo and C. R. Indrati, On Conformable
Fractional Riesz Bounded p-Variation of Order- .- H. K. Ningrum, E. Y.
Asmarani, I Gede Adhitya Wisnu Wardhana, S. Salwa and Z. Y. Awanis, The
Wiener Index, The Harmonic Index, and The Graph Representation of the Prime
Ideal Graph for the Integers Modulo Rings with Prime Power Order.- R.
Rinurwati, M. Chalid Fansury, A. Hevita G.K. Saefulloh and T. I. Haryadi,
Multiplicative Sum Nano Zagreb Index of Various 2-Power Corona Graphs.
Pages: 188
Illustrated by: Alexander Lu
ISBN: 978-981-12-8759-6 (hardcover)
ISBN: 978-981-12-8802-9 (softcover)
Embark on a whimsical odyssey through the realms of logic, game theory, paradoxes, biases, fake data detection, graph theory, AI bots and so much more! Within these pages you will find a collection of fictional short stories that weave together the intriguing, the counterintuitive and the downright quirky, with bold characters from every walk of life. Each chapter is written in a unique style, sprinkled throughout with anecdotes, open questions and fun exercises and to tickle the mind.
When Pigs Fly
Ultra-Altruism
Fakebook
Deadly Serious Party
The Forever Virus
Ending the Forever Virus
Explosive Logic
CONcrete Evidence
Existential Overload
Blue Album
Infinity and Beyond
All undergraduate and students in the second half of high school, particularly in the fields of mathematics, computer science, engineering, economics, business, political science, and social science; General public who are curious about the intricacies and counterintuitive nature of reality.