Available for pre-order. Item will ship after June 1, 2020
ISBN 9781138311923
June 1, 2020 Forthcoming by A K Peters/CRC Press
192 Pages - 620 Color Illustrations
This new edition of Six Simple Twists: The Pleat Pattern Approach to Origami Tessellation Design introduces an innovative
pleat pattern technique for origami designs that is easily accessible to anyone who enjoys the geometry of paper. The book
begins with six basic forms meant to ease the reader into the style, and then systematically scaffolds the instructions to
build a strong understanding of the techniques, leading to instructions on a limitless number of patterns. It then describes
a process of designing additional building blocks. At the end, what emerges is a fascinating art form that will enrich
folders for many years. Unlike standard, project-based origami books, Six Simple Twists focuses on how to design, rather than
construct.
In this thoroughly updated second edition, the book explores new techniques and example tessellations, with full-page images,
and mathematical analysis of the patterns. A reader will, through practice, gain the ability to create still more complex and
Part I
1.00 - Why Study Pleat Patterns?
1.01 - Basics and Preparation
1.02 - How Pleat Patterns Differ from Traditional Origami
1.03 - How to Read the Diagrams and Fold Parity
1.04 - Folding Uniform Parallel Creases
1.05 - Grid Axes and How to Fold a Hexagon
1.06 - How to Fold a Triangle Grid
1.07 - Simple Pleat
1.08 - The Six Simple Twists
1.09 - Triangle Twist
1.10 - Triangle Spread
1.11 - Hex Twist
1.12 - Hex Spread
1.13 - Rhombic Twist
1.14 - Arrow Twist
1.15 - Anatomy of a Molecule
1.16 - Pleat Intersection Notation
Part II
2.00 - How to Use the Six Simple Twists
2.01 - 32ndfs Grid
2.02 - Locking and Unlocking Pleats
2.03 - Triangle Twist Tessellation
2.04 - 3.6.3.6 Tessellation
2.05 - Tessellation Basics
2.06 - Applying Tessellation Knowledge Folding
2.07 - Triangle Weave Tessellation
2.08 - 3.6.3.6 Weave Tessellation
2.09 - 6.6.6 Hexagonal Failing Cluster
2.10 - Modifications
2.11 - Backtwisting
2.12 - Twist Handedness and Pleat Symmetry
2.13 - Pleat Flattening
2.14 - Triangle Twist Tessellation with Flattened Pleats
2.15 - Hidden Circles Pattern
2.16 - Rhombic Twist Tessellation
2.17 - Rhombic Twist Variants
2.18 - Twist Sinking
2.19 - Twist Expansion
2.20 - Nub Offset Tessellation
2.21 - Shift Rosette Tessellation
2.22 - Ridge Creation
2.23 - Button Molecule
2.24 - Button Molecule Tessellation
2.25 - Triangle Flagstone Tessellation and Offsetting Pleats
2.26 - 3.6.3.6 Flagstone Tessellation
2.27 - Crooked Split
2.28 - Snowflake Tessellation
2.29 - Tulip Split
2.30 - Tulip Split Tessellation
2.31 - Molecule Size and Different Grid Densities
2.32 - gFronth and gBackh Sides
2.33 - Tendril Tessellation
2.34 - Inverting a Pleat
2.35 - Iso-Area Triangle Twist Tessellation
2.36. - Pleat Pushing
2.37 - Platform Tess
2.38 - Triple Twist Tess
Part III
3.00 - Pleat Patterns as Artwork
3.01 - Gallery
3.02 - Pleat-to-Molecule Analysis
3.03 - Twist Archetype Sets
3.04 - Molecule Database
3.05 - Archetype Composition
3.06 - Actions and Notation
3.07 - Splitting Equation
3.08 - Normal Polygon Models
3.09 - Circle Cutout Model
3.10 - Molecule-to-Pleat Analysis
3.11 - Sectioning Model of Perfect Twist Design
3.12 - Brocard Points
Available for pre-order. Item will ship after July 6, 2020
ISBN 9780367464325
July 6, 2020 Forthcoming by Chapman and Hall/CRC
295 Pages - 25 B/W Illustrations
Multiple Fixed-Point Theorems and Applications in the Theory of ODEs, FDEs and PDEs covers all the basics of the subject of
fixed-point theory and its applications with a strong focus on examples, proofs and practical problems, thus making it ideal
as course material but also as a reference for self-study.
Many problems in science lead to nonlinear equations T x + F x = x posed in some closed convex subset of a Banach space. In
particular, ordinary, fractional, partial differential equations and integral equations can be formulated like these abstract
equations. It is desirable to develop fixed-point theorems for such equations. In this book, the authors investigate the
existence of multiple fixed points for some operators that are of the form T + F, where T is an expansive operator and F is a
k-set contraction. This book offers the reader an overview of recent developments of multiple fixed-point theorems and their
applications.
1. Fixed Point Index Theory. Multiple Fixed Point Theorems 1.1 Measures of Noncompactness 1.2 The Brower Fixed Point Theorem.
The Schauder Fixed Point Theorem 1.3 Fixed Points of Strict Set Contractions 1.4 The Kronecker Index 1.5 The Brower Degree
1.5.1 Smooth Mappings 1.5.2 Homotopy Invariance 1.5.3 Continuous Mappings. Basic Properties 1.5.4 The Case f : D _ Rn !Sn1
1.6 The Leray-Schauder Degree 1.7 The Fixed Point Index for Completely Continuous Mappings 1.8 The Fixed Point Index for
Strict Set Contractions 1.9 Multiple Fixed Point Theorems 2. Applications to ODEs 2.1 Periodic Solutions for First Order ODEs
2.2 BVPs for First Order ODEs 2.3 BVPs for Second Order ODEs 2.4 BVPs with Impulses 3. Applications to FDEs 3.1 Global
existence for a class fractional-differential equations 3.2 Multiple Solutions for a BVP of Nonlinear Riemann-Liouville
Fractional Differential Equations . 3.3 Multiple Solutions for a BVP of Nonlinear Caputo Fractional Differential Equations 4.
Applications to Parabolic Equations 4.1 Differentiability of the Classical Solutions with Respect to the Initial Conditions
of an IVP 4.2 Local Existence of Classical Solutions for an IBVP 4.3 Periodic Solutions 4.4 Multiple Solutions for an IBVP
with Robin Boundary Conditions 5. Applications to Hyperbolic Equations 5.1 Differentiability of the Classical Solutions with
Respect to the Initial Conditions for an IVP for a Class Hyperbolic Equations 5.2 Multiple Solutions for an IBVP with Robin
Boundary Conditions 5.3 Periodic Solutions 6. Applications to Elliptic Equations 6.1 Multiple Solutions for an BVP with Robin
Boundary Conditions 6.2 Existence and Smoothness of Navier-Stokes Equations References
Available for pre-order. Item will ship after June 8, 2020
ISBN 9780367459154
June 8, 2020 Forthcoming by Chapman and Hall/CRC
424 Pages
Morrey spaces were introduced by Charles Morrey to investigate the local behaviour of solutions to second order elliptic
partial di?erential equations. The technique is very useful in many areas in mathematics, in particular in harmonic analysis,
potential theory, partial di?erential equations and mathematical physics.
Across two volumes, the authors of Morrey Spaces: Introduction and Applications to Integral Operators and PDEfs discuss the
current state of art and perspectives of developments of this theory of Morrey spaces, with the emphasis in Volume II focused
mainly generalizations and interpolation of Morrey spaces.
Provides a efrom-scratchf overview of the topic readable by anyone with an understanding of integration theory
Suitable for graduate students, masters course students, and researchers in PDE's or Geometry
Replete with exercises and examples to aid the readerfs understanding
Table of Contents
11. Multilinear operators and Morrey spaces. 12. Generalized Morrey/Morrey-Campanato spaces. 13. Generalized Orlicz-Morrey
spaces. 14. Morrey spaces over metric measure spaces. 15. Weighted Morrey spaces. 16. Morrey-type spaces. 17. Pointwise
product. 18. Real interpolation of Morrey spaces. 19. Complex interpolation of Morrey spaces. Bibliography. Index.
Available for pre-order. Item will ship after June 30, 2020
ISBN 9781315898582
June 30, 2020 Forthcoming by Chapman and Hall/CRC
248 Pages
Since their appearance in mid-1980s, wavelets and, more generally, multiscale methods have become powerful tools in
mathematical analysis and in applications to numerical analysis and signal processing. This book is based on "Ondelettes et
Traitement Numerique du Signal" by Albert Cohen. It has been translated from French by Robert D. Ryan and extensively updated
by both Cohen and Ryan. It studies the existing relations between filter banks and wavelet decompositions and shows how these
relations can be exploited in the context of digital signal processing. Throughout, the book concentrates on the
fundamentals. It begins with a chapter on the concept of multiresolution analysis, which contains complete proofs of the
basic results. The description of filter banks that are related to wavelet bases is elaborated in both the orthogonal case
(Chapter 2), and in the biorthogonal case (Chapter 4). The regularity of wavelets, how this is related to the properties of
the filters and the importance of regularity for the algorithms are the subjects of Chapter 3. Chapter 5 looks at multiscale
decomposition as it applies to stochastic processing, in particular to signal and image processing.
1. Multiresolution Analysis. Introduction 2. Wavelets and Conjugate Quadrature Filters 3. The Regularity of Scaling Functions
and Wavelets 4. Biorthogonal Wavelet Bases 5. Stochastic Processes. A Quasi-Analytic Wavelet Bases. B Multivariate
Constructions. C Multiscale Unconditional Bases. D Notation.