Format: Paperback / softback, 85 pages, height x width: 235x155 mm, VII, 85 p., 1 Paperback / softback
Series: SpringerBriefs in Statistics
Pub. Date: 12-Jul-2022
ISBN-13: 9783030998875
This book discusses important applications of the Behrens-Fisher statistic and the False Discovery Rate (FDR). Covered applications include ANOVA and MANOVA under potentially non-normal errors and heteroscedasticity; and an intuitive method of analyzing s x r contingency tables when the column variable is ordinal. This book also explores the novel possibility that these applications may be deemed nonparametric.
1. Introduction.-
2. An Introduction to the Bootstrap.-
3. An Introduction to the False Discovery Rate.-
4. Application to ANOVA and MANOVA.-
5. Application to Testing Equality of Several Variances and Several Covariance Matrices.-
6. Application to Testing Equality of Several Medians.-
7. Testing for Symmetry of Univariate Distributions and Central Symmetry of Multivariate Distributions.
Format: Paperback / softback, 134 pages, height x width: 235x155 mm, weight: 238 g, XII, 134 p., 1 Paperback / softback
Pub. Date: 30-May-2022
ISBN-13: 9783030737207
This book presents the foundation of the theory of almost automorphic functions in abstract spaces and the theory of almost periodic functions in locally and non-locally convex spaces and their applications in differential equations. Since the publication of Almost automorphic and almost periodic functions in abstract spaces (Kluwer Academic/Plenum, 2001), there has been a surge of interest in the theory of almost automorphic functions and applications to evolution equations. Several generalizations have since been introduced in the literature, including the study of almost automorphic sequences, and the interplay between almost periodicity and almost automorphic has been exposed for the first time in light of operator theory, complex variable functions and harmonic analysis methods. As such, the time has come for a second edition to this work, which was one of the most cited books of the year 2001.
This new edition clarifies and improves upon earlier materials, includes many relevant contributions and references in new and generalized concepts and methods, and answers the longtime open problem, "What is the number of almost automorphic functions that are not almost periodic in the sense of Bohr?" Open problems in non-locally convex valued almost periodic and almost automorphic functions are also indicated.
As in the first edition, materials are presented in a simplified and rigorous way. Each chapter is concluded with bibliographical notes showing the original sources of the results and further reading.
1. Introduction and Preliminaries.-
2. Almost Automorphic Functions.-
3. Almost Automorphy of the Function f(t,x).-
4. Differentiation and Integration.-
5. Pseudo Almost Automorphy.-
6. Stepanov-like Almost Automorphic Functions.-
7. Dynamical Systems and C0-Semigroups.-
8. Almost Periodic Functions with Values in a Locally Convex Space.-
9. Almost Period Functions with Values in a Non-Locally Convex Space.-
10. The Equation x'(t)=A(t)x(t)+f(t).-
11. Almost Periodic Solutions of the Differential Equation in Locally Convex Spaces.- Bibliography.
Format: Hardback, 216 pages, height x width: 235x155 mm, 25 Tables, color; 91 Illustrations, color;
29 Illustrations, black and white; XIV, 216 p. 120 illus., 91 illus. in color., 1 Hardback
Series: Emergence, Complexity and Computation 45
Pub. Date: 13-Aug-2022
ISBN-13: 9783031039850
This book brings together the impact of Prof. John Horton Conway, the playful and legendary mathematician's wide range of contributions in science which includes research areas?Game of Life in cellular automata, theory of finite groups, knot theory, number theory, combinatorial game theory, and coding theory. It contains transcripts where some eminent scientists have shared their first-hand experience of interacting with Conway, as well as some invited research articles from the experts focusing on Game of Life, cellular automata, and the diverse research directions that started with Conway's Game of Life. The book paints a portrait of Conway's research life and philosophical direction in mathematics and is of interest to whoever wants to explore his contribution to the history and philosophy of mathematics and computer science. It is designed as a small tribute to Prof. Conway whom we lost on April 11, 2020.
Format: Paperback / softback, 928 pages, height x width: 235x155 mm, 119 Illustrations, color;
12 Illustrations, black and white; X, 928 p. 131 illus., 119 illus. in color
Series: Lecture Notes on Mathematical Modelling in the Life Sciences
Pub. Date: 23-Aug-2022
ISBN-13: 9783030981358
This book provides an introduction to the theory of ordinary differential equations and its applications to population dynamics.
Part I focuses on linear systems. Beginning with some modeling background, it considers existence, uniqueness, stability of solution, positivity, and the Perron?Frobenius theorem and its consequences.
Part II is devoted to nonlinear systems, with material on the semiflow property, positivity, the existence of invariant sub-regions, the Linearized Stability Principle, the Hartman?Grobman Theorem, and monotone semiflow.
Part III opens up new perspectives for the understanding of infectious diseases by applying the theoretical results to COVID-19, combining data and epidemic models. Throughout the book the material is illustrated by numerical examples and their MATLAB codes are provided.
Bridging an interdisciplinary gap, the book will be valuable to graduate and advanced undergraduate students studying mathematics and population dynamics.
Part I Linear Differential and Difference Equations: 1 Introduction to Linear Population Dynamics.- 2 Existence and Uniqueness of Solutions.- 3 Stability and Instability of Linear Systems.- 4 Positivity and Perron-Frobenius Theorem.- Part II NonLinear Differential: 5 Nonlinear Differential Equation.- 6 The Linearized Stability Principle and the Hartman-Grobman Theorem.- 7 Positivity and Invariant Sub-Regions.- 8 Monotone Semiflows.- Part III Applications to Epidemic Models: 9 Understanding and Predicting Unreported Cases in the 2019-nCov Epidemic Outbreak in Wuhan, China, and the Importance of Major Public Health Interventions.- 10 The COVID-19 Outbreak in Japan: Unreported Age-Dependent Cases.- 11 Clarifying Predictions for COVID-19 from Testing Data: The Example of New York State.- 12 SI Epidemic Model Applied to COVID-19 Data in Mainland China.- 13 A Robust Phenomenological Approach to Investigating COVID-19 Data for France.- 14 What Can We Learn From COVID-19 Data By Using Epidemic Models With Unidentified Infectious Cases?.- 15 Supplementary material.
Format: Hardback, 320 pages, height x width: 235x155 mm, 25 Tables, color; 30 Illustrations, color;
27 Illustrations, black and white; XII, 320 p. 57 illus., 30 illus. in color., 1 Hardback
Series: Theoretical and Mathematical Physics
Pub. Date: 03-Sep-2022
ISBN-13: 9789811932618
Quantum groups have been studied intensively in mathematics and have found many valuable applications in theoretical and mathematical physics since their discovery in the mid-1980s. Roughly speaking, there are two prototype examples of quantum groups, denoted by Uq and Aq. The former is a deformation of the universal enveloping algebra of a Kac-Moody Lie algebra, whereas the latter is a deformation of the coordinate ring of a Lie group. Although they are dual to each other in principle, most of the applications so far are based on Uq, and the main targets are solvable lattice models in 2-dimensions or quantum field theories in 1+1 dimensions. This book aims to present a unique approach to 3-dimensional integrability based on Aq. It starts from the tetrahedron equation, a 3-dimensional analogue of the Yang-Baxter equation, and its solution due to work by Kapranov-Voevodsky (1994). Then, it guides readers to its variety of generalizations, relations to quantum groups, and applications. They include a connection to the Poincare-Birkhoff-Witt basis of a unipotent part of Uq, reductions to the solutions of the Yang-Baxter equation, reflection equation, G2 reflection equation, matrix product constructions of quantum R matrices and reflection K matrices, stationary measures of multi-species simple-exclusion processes, etc. These contents of the book are quite distinct from conventional approaches and will stimulate and enrich the theories of quantum groups and integrable systems.
Introduction.- Tetrahedron equation.- 3D R from quantized coordinate ring of type A.- 3D reflection equation and quantized reflection equation.- 3D K from quantized coordinate ring of type C.- 3D K from quantized coordinate ring of type B.- Intertwiners for quantized coordinate ring Aq (F4).- Intertwiner for quantized coordinate ring Aq (G2).- Comments on tetrahedron-type equation for non-crystallographic Coxeter groups.- Connection to PBW bases of nilpotent subalgebra of Uq.- Trace reductions of RLLL = LLLR.- Boundary vector reductions of RLLL = LLLR.- Trace reductions of RRRR = RRRR.- Boundary vector reductions of RRRR = RRRR.- Boundary vector reductions of (LGLG)K = K(GLGL).- Reductions of quantized G2 reflection equation.- Application to multispecies TASEP.
Format: Paperback / softback, 181 pages, height x width: 235x155 mm, 21 Tables, color;
27 Illustrations, color; 23 Illustrations, black and white; VIII, 181 p. 50 illus., 27 illus. in color
Series: Surveys and Tutorials in the Applied Mathematical Sciences 10
Pub. Date: 11-Aug-2022
ISBN-13: 9783031058202
This book develops a class of graded finite element methods to solve singular elliptic boundary value problems in two- and three-dimensional domains. It provides an approachable and self-contained presentation of the topic, including both the mathematical theory and numerical tools necessary to address the major challenges imposed by the singular solution. Moreover, by focusing upon second-order equations with constant coefficients, it manages to derive explicit results that are accessible to the broader computation community. Although written with mathematics graduate students and researchers in mind, this book is also relevant to applied and computational mathematicians, scientists, and engineers in numerical methods who may encounter singular problems.
The Finite Element Method.- The Function Space.- Singularities and Graded Mesh Algorithms.- Error Estimates in Polygonal Domains.- Regularity Estimates and Graded Meshes in Polyhedral Domains.- Anisotropic Error Estimates in Polyhedral Domains.