Format: Hardback, 292 pages, height x width: 235x155 mm, 3 Illustrations,
color; 3 Illustrations, black and white; VIII, 292 p. 6 illus., 3 illus. in color.
Series: Springer Proceedings in Mathematics & Statistics 440
Pub. Date: 09-Apr-2024
ISBN-13: 9783031505850
This proceedings contains a collection of selected, peer-reviewed contributions from the 4th International Workshop "Differential Geometric Structures and Applications" held in Haifa, Israel from May 10?13, 2023. The papers included in this volume showcase the latest advancements in modern geometry and interdisciplinary applications in fields ranging from mathematical physics to biology.
Since 2008, this workshop series has provided a platform for researchers in pure and applied mathematics, including students, to engage in discussions and explore the frontiers of modern geometry. Previous workshops in the series have focused on topics such as "Reconstruction of Geometrical Objects Using Symbolic Computations" (2008), "Geometry and Symbolic Computations" (2013), and "Geometric Structures and Interdisciplinary Applications" (2018).
1.Some topics in Sasakian geometry, a survey ( A.
Tralle).- 2.Einstein-type metrics and Ricci-type solitons on weak f-K-contact
(V. Rovenski).- 3.Weak -Kenmotsu manifolds and -Ricci solitons (D.S. Patra,
V. Rovenski).- 4.Twistor bundles of foliated Riemannian manifolds (R. Mohseni
and R. Wolak).- 5.Mixed 3-Sasakian statistical manifolds and statistical
submersions (C.D. Neacosu).- 6.Minimal unit vector elds on oscillator
groups (A. Yampolsky).- 7.Growth and structure of equicontinuous foliated
spaces (M.F. Moreira).- 8.Lichnerowicz-type Laplacians in the Bochner
technique (V. Rovenski, S. Stepanov and I. Tsyganok).- 9.On general solutions
of Sinyukov equations on two-dimensional equidistant (pseudo-)Riemannian
spaces (P. Peska, L. VLtkovLa, J. Mikes and I. Kuzmina).- 10.Fundamental
equations on conformal Fedosov spaces (C. Almazbekov, N. Guseva and J.
Mikes).- 11.Rotary mappings of equidistant spaces (L.
VLtkovLa).- 12.Smith-Gysin sequence (J.I.R. Prieto, M. Saralegi-Aranguren,
and R. Wolak) .- 13.An Ay-Le-Jost-SchwachhOofer type characterization of
quantitatively weakly sucient statistics (K. Yamaguchi and H.
Nozawa).- 14.Lower bounds for high derivatives of smooth functions with given
zeros (G. Goldman and Y. Yomdin).- 15.Interactions between dierential
geometry and production theory (A.D. Vlcu and G.E. Vlcu).- 16.A
Lagrangian program detecting the weighted Fermat-Steiner-FrLechet multitree
for a FrLechet N-multisimplex in Euclidean N-space (A.N Zachos).
Format: Hardback, 364 pages, height x width: 235x155 mm, 5 Illustrations, black and white; X, 364 p. 5 illus.,
Series: Springer Proceedings in Mathematics & Statistics 447
Pub. Date: 23-Apr-2024
ISBN-13: 9789819995059
This volume consists of 15 papers contributing to the Hayama Symposium on Complex Analysis in Several Variables XXIII, which was dedicated to the 100th anniversary of the creation of the Bergman kernel. The symposium took place in Hayama and Tokyo in July 2022. Each article is closely related to the Bergman kernel, covering topics in complex analysis, differential geometry, representation theory, PDE, operator theory, and complex algebraic geometry.
Specifically, some papers address the L2 extension operators from a newly opened viewpoint after solving Suita's conjecture for the logarithmic capacity. They are also continuations of quantitative solutions to the openness conjecture for the multiplier ideal sheaves. The study involves estimates for the solutions of the d-bar equations, focusing on the existence of compact Levi-flat hypersurfaces in complex manifolds.
The collection also reports progress on various topics, including the existence of extremal Kahler metrics on compact manifolds, Lp variants of the Bergman kernel, Wehrl-type inequalities, homogeneous Kahler metrics on bounded homogeneous domains, asymptotics of the Bergman kernels, and harmonic Szeg kernels and operators on the Bergman spaces and Segal-Bargmann spaces.
Some of the papers are written in an easily accessible way for beginners. Overall, this collection updates how a basic notion provides strong insights into the internal relationships between independently found phenomena.
S. Bao, Q. Guan, Zhitong Mi and Z. Yuan. Concavity property of minimal
L^2 integrals with Lebesgue measurable gain VIINegligible weights.- P.
Blaschke and M. Engli, M-harmonic Szego kernel on the ball.- Bo-Yong Chen,
Y. Xiong and L. Zhang, Some aspects of the p-Bergman theory.- S. Finski, On
semiclassical Ohsawa-Takegoshi extension theorem.- Y. Hashimoto, Balanced
metrics for extremal Kahler metrics and Fano manifolds.- F. Haslinger,
Unbounded operators on the Segal-Bargmann space.- T. Hisamoto, Asymptotic
construction of the optimal degeneration for a Fano manifold.- Chin-Yu Hsiao
and G. Marinescu, Semi-classical spectral asymptotics of Toeplitz operators
on strictly pseudodonvex domains.- H. Ishi, On a concrete realization of
simply connected complex domains admitting homogeneous Kahler metrics.- J.
Kamimoto, The asymptotic behavior of the Bergman kernel on pseudoconvex model
domains.- T. Ohsawa, Bundle-convexity and kernel asymptotics on a class of
locally pseudoconvex domains.- Mei-Chi Shaw, The dbar-equation on the Hartogs
triangles in C^2 and CP^2.- H. Tsuji, Dynamical systems of p-Bergman
kernels.- G. Zhang, Wehrl-type inequalities for Bergman spaces on domains in
C^d and completely positive maps.- X. Zhou , Converse of L^2 existence and
extension of cohomology classes.
Pages: 250
ISBN: 978-981-12-8762-6 (hardcover)
This unique volume covers two fundamental elements of computational methods ? numbers and functions. It provides an in-depth discussion of the behaviors of numbers, including both real and complex numbers. The discussion leads to the important closure properties of numbers, ensuring solution consistence and existence, and also possible failure in numerical computations in science and engineering.
This text then introduces types of functions that take numbers as independent variables and produce a single number. Approaches for constructing inverse functions are also provided. Frequently used basis functions are introduced, with detailed studies on their properties and behaviors. Techniques are presented for constructing basis functions and their use in function approximation in computational methods.
Introduction
Real Numbers
Complex Numbers
Elementary Functions
Basis Functions
Function Approximation
Researchers, professionals, academics and graduate students in numerical analysis and mathematical computation.
Pages: 298
ISBN: 978-981-12-8600-1 (hardcover)
One of the central highlights of this work is the exploration of the Yoneda lemma and its profound implications, during which intuitive explanations are provided, as well as detailed proofs, and specific examples. This book covers aspects of category theory often considered advanced in a clear and intuitive way, with rigorous mathematical proofs. It investigates universal properties, coherence, the relationship between categories and graphs, and treats monads and comonads on an equal footing, providing theorems, interpretations and concrete examples. Finally, this text contains an introduction to monoidal categories and to strong and commutative monads, which are essential tools in current research but seldom found in other textbooks.
Starting Category Theory serves as an accessible and comprehensive introduction to the fundamental concepts of category theory. Originally crafted as lecture notes for an undergraduate course, it has been developed to be equally well-suited for individuals pursuing self-study. Most crucially, it deliberately caters to those who are new to category theory, not requiring readers to have a background in pure mathematics, but only a basic understanding of linear algebra.
Preface:
How to Read This Book
About This Work
Sources
Acknowledgements
Basic Concepts:
Categories
Mono and Epi
Functors
Natural Transformations
Studying Categories by Means of Functors
The Yoneda Lemma:
Representable Functors and the Yoneda Embedding Theorem
Statement and Proof of the Yoneda Lemma
Universal Properties
Limits and Colimits:
General Definitions
Particular Limits and Colimits
Functors, Limits and Colimits
Limits and Colimits of Sets
Adjunctions:
General Definitions
Unit and Counit
The Adjoint Functor Theorem for Preorders
The Case of Convex Subsets
Monads and Comonads:
Monads as Extensions of Spaces
Monads as Theories of Operations
Comonads as Extra Information
Comonads as Processes on Spaces
Adjunctions, Monads and Comonads
Monoidal Categories:
General Definitions
Monoids and Comonoids
Monoidal Functors
Monads on Monoidal Categories
Closed Monoidal Categories
Conclusion:
Further Reading
Online Resources
Bibliography
Index
This book is primarily targeted towards undergraduate and graduate students in mathematics and related fields (physics, computer science, statistics, engineering),
and is suitable for either course adoption for category theory and discrete mathematics, or for self-study. More broadly,
this book can appeal to researchers in related fields and professionals working in technology (machine learning, etc.).
Pages: 364
ISBN: 978-1-80061-526-7 (hardcover)
ISBN: 978-1-80061-537-3 (softcover)
The calculus of variations is one of the oldest subjects in mathematics, and it is very much alive and still evolving. Besides its mathematical importance and its links to other branches of mathematics, such as geometry or differential equations, it is widely used in physics, engineering, economics and biology.
This book serves both as a guide to the expansive existing literature and as an aid to the non-specialist ? mathematicians, physicists, engineers, students or researchers ? in discovering the subject's most important problems, results and techniques. Despite the aim of addressing non-specialists, mathematical rigor has not been sacrificed; most of the theorems are either fully proved or proved under more stringent conditions.
This new edition offers an entirely new chapter, as well as the addition of several new exercises. The book, containing a total of 147 exercises with detailed solutions, is well designed for a course at both undergraduate and graduate levels.
Preface to the Fourth English Edition
Introduction
Preliminaries
Classical Methods
Direct Methods: Existence
Direct Methods: Regularity
Minimal Surfaces
Isoperimetric Inequality
Geodesic
Solutions to the Exercises
Bibliography
Index
This book is suitable for advanced undergraduate and graduate students, as well as researchers in the field of calculus of variations
and differential equations. It would also be applicable to physicists, engineers economists or biologists more generally who are interested in mathematics.