Format: Hardback, 789 pages, height x width: 235x155 mm, 448 Illustrations, black and white; XX, 760 p. 451 illus., 12 illus. in color.,
Series: Sources and Studies in the History of Mathematics and Physical Sciences
Pub. Date: 03-Jan-2025
ISBN-13: 9783031725845
This monograph traces the development of projective geometry from its Greek origins to the early 20th century. It covers Renaissance perspective studies and insights from the late sixteenth to seventeenth centuries, examining the contributions of Desargues and Pascal.
Most of the book is devoted to the evolution of the subject in the 19th century, from Carnot to von Staudt. In particular, the book offers an unusually thorough appreciation of Brianchon's work, a detailed study of Poncelet's innovations, and a remarkable account of the contributions of Mobius and Plucker. It also addresses the difficult question of the historical relationship between synthetic and analytic points of view in geometry, analyzing the work of prominent synthetic geometers Steiner, Chasles, and von Staudt in detail. The book concludes around 1930, after the synthetic point of view was axiomatized and the analytic point of view became intertwined with algebraic geometry.
Balancing historical analysis with technical precision and providing deep insights into the evolution of the mathematics, this richly illustrated book serves as a central reference on the history of projective geometry.
1. The Greek Legacy.-
2. Perspective in the Renaissance.-
3. New ways
of looking at conics.-
4. Desargues, the dawn of projective geometry.-
5. Pascals geometrical achievements.-
6. An interlude a century and a half long.-
7. Towards a new geometry.-
8. Poncelet, the projective properties of figures.-
9. The algebraic way to projective geometry.-
10. The synthetic route: the contributions of Steiner and Chasles.-
11. Von Staudts pure synthetism.-
12. Projective geometry 1870-1930 and beyond.
Format: Paperback 288 pages, height x width: 235x155 mm, 45 Illustrations, black and white; Approx. 280 p. 41 illus., 1 illus. in color.,
Pub. Date: 14-Jan-2025
ISBN-13: 9783031711480
This second edition of "The Geometry of Special Relativity - a Concise Course" offers more than just corrections and enhancements. It includes a new chapter on four-velocities and boosts as points and straight lines of hyperbolic geometry. Quantum properties of relativistic particles are derived from the unitary representations of the Poincare group. Notably, the massless representation is related to the concept of a Hopf bundle. Scattering theory is developed analogously to the non-relativistic case, relying on proper symmetry postulates. Chapters on quantum fields, reflections of charge, space, and time, and the necessary gauge symmetry of quantized vector fields complete the foundation for evaluating Feynman graphs. An extended appendix covers more than a dozen additional topics.
The first half of this edition refines the first edition, using simple diagrams to explain time dilation, length contraction, and Lorentz transformations based on the invariance of the speed of light. The text derives key results of relativistic physics and resolves apparent paradoxes. Following a presentation of the action principle, Noether's theorem, and relativistic mechanics, the book covers the covariant formulation of electrodynamics and classical field theory. The groups of rotations and Lorentz transformations are also examined as a transition to relativistic quantum physics.
This text is aimed at graduate students of physics and mathematics seeking an advanced introduction to special relativity and related topics. Its presentation of quantum physics aims to inspire fellow researchers.
Structures of Spacetime.- Time and
Distance.- Transformations.- Relativistic
Particles.- Electrodynamics.- Classical Field Theory.- The Lorentz
Group.-Hyperbolic and Spherical Geometry.- Relativistic Quantum
Physics.- Scattering.- Quantum Fields.- Space Inversion, Time Reversal,
Charge Conjugation.- Gauge Symmetry.- Appendix A, B, C, D.- References.-
Index.
Format: Paperback 396 pages, height x width: 240x168 mm, 2 Illustrations, color; 3 Illustrations, black and white; Approx. 355 p.,
Series: Frontiers in Mathematics
Pub. Date: 20-Feb-2025
ISBN-13: 9783031717000
Mainly addressed to researchers in the fields of generalized measure theory, nonlinear integrals, nonlinear functional analysis, and nonlinear approximation theory, this book is based mainly on the authorsf results. While the Choquet integral has proven to be powerful and useful in cooperative games, decision theory, finance, economics, insurance, pattern recognition, artificial intelligence, and automated reasoning, these applications are not the focus in this monograph. Instead, the special properties of Choquetfs integral, inspired the study of various aspects for the class of monotone sublinear operators (more general than the positive linear operators) on Banach ordered spaces, as for example Korovkin-type results. The main ideas in this book also include the replacement in various known mathematical concepts, of the classical linear Lebesgue integral by the nonlinear (sublinear and monotone) Choquet integral and to study the new obtained concepts.
Choquet Integral.- Choquet-Bochner Integral.- Choquet Integral in
Capacity.- Choquet-Stieltjes Integrals on Intervals.- Other Generalizations.-
Choquet Type Integral Equations and Operators.- Constructive Approximation
Involving Choquet Integrals.- Korovkin-Type Theorems for Monotone Sublinear
Operators.- A Few Elements of Functional Analysis for Sublinear and Monotone
Operators.
Format: Hardback, 375 pages, height x width: 235x155 mm, X, 352 p.,
Series: Indian Statistical Institute Series
Pub. Date: 08-Jan-2025
ISBN-13: 9789819779284
This book covers major measure theory topics with a fairly extensive study of their applications to probability and analysis. It begins by demonstrating the essential nature of measure theory before delving into the construction of measures and the development of integration theory. Special attention is given to probability spaces and random variables/vectors. The text then explores product spaces, RadonNikodym and JordanHahn theorems, providing a detailed account of ???? spaces and their duals. After revisiting probability theory, it discusses standard limit theorems such as the laws of large numbers and the central limit theorem, with detailed treatment of weak convergence and the role of characteristic functions.
The book further explores conditional probabilities and expectations, preceded by motivating discussions. It discusses the construction of probability measures on infinite product spaces, presenting Tulceas theorem and Kolmogorovs consistency theorem. The text concludes with the construction of Brownian motion, examining its path properties and the significant strong Markov property. This comprehensive guide is invaluable not only for those pursuing probability theory seriously but also for those seeking a robust foundation in measure theory to advance in modern analysis. By effectively motivating readers, it underscores the critical role of measure theory in grasping fundamental probability concepts.
1. Measure Theory: Why and What.- 2. Measures: Construction and
Properties.- 3. Measurable Functions and Integration.- 4. Random Variables
and Random Vectors.- 5. Product Spaces.- 6. Radon-Nikodym Theorem and Lp
Spaces.- 7. Convergence and Laws of Large Numbers.- 8. Weak convergence and
Central Limit Theorem.- 9. Conditioning: The Right Approach.- 10. Infinite
Products.- 11. Brownian Motion: A Brief Journey.
Format: Hardback, 420 pages, height x width: 235x155 mm, 94 Illustrations, color; 15 Illustrations, black and white; X, 420 p. 107 illus., 95 illus. in color.
Series: Springer Proceedings in Mathematics & Statistics 469
Pub. Date: 26-Dec-2024
ISBN-13: 9783031689482
This volume showcases a collection of thirty-two peer-reviewed articles presented at the XXVI Congress of the Portuguese Statistical Society (2023). It covers a wide range of cutting-edge topics in both theoretical and applied statistics. Each contribution highlights the latest advancements and research in the field, offering valuable insights and innovative methodologies for researchers and practitioners alike. Readers with a background in mathematics and statistics will find it particularly beneficial, while researchers from various scientific disciplines can explore numerous robust applications.
A note on a ParzenRosenblatt type density estimator for circular
data.- Population Growth and Geometrically Thinned Extreme Value Theory.- An
additive shared frailty model for recurrent gap time data in the presence of
zero-recurrence subjects.- Clustering and Risk Analysis for evaluating the
water quality of a hydrological basin.- Green Exchange-Traded Fund
Performance Evaluation Using the EU-EV Risk Model.- Risk Assessment of
Vulnerabilities Exploitation.- Bayesian modelling of time series of counts
with missing data.- Sexual Classification Based on Orthopantomographs.-
Survapp: a Shiny Application for Survival Data Analysis.- An Application of
Multivariate Random Fields and Systems of Stochastic Partial Differential
Equations to Wind Velocity Data.- A direct approach in extremal index
estimation.- When PACE-Gate Meets Sample Size Calculations.- An Approach for
Predicting Spatially Indexed Carcass Persistence Probability to Estimate Bird
Mortality at Power Lines.- Extremal Behavior of Some Bivariate Integer
Models.- Solar Radiation Forecasting: A Study Case in the Colombian Caribbean
Region.- Sources of bias when assessing seasonal influenza vaccine
performance: a narrative review.- Peaks Over Random Thresholds (PORT)
Estimation of the Weibull Tail Coefficient.- Exploring the Mutual Information
Rate Decomposition in Situations of Pathological Stress.- A Simulation
Comparison of Spatial Models for Preferential Sampling.- A Partially Reduced
Bias Hill Estimator of the Extreme Value Index.- The importance of
experimental design principles in agricultural field trials: a note for
grapevine field trials.- A new class of conditional tail expectation
estimators.- Tail (In)dependence: a Comparative Analysis of Estimation
Methods.- Robust Estimation for the Random Effects Panel Data Models.- Air
Quality Data Analysis with Symbolic Principal Components.- Geostatistical
Models for Identifying Juvenile Fish Hotspots in Marine Conservation.- Count
Models and Randomness Patterns.- Neurological Disease Classification based on
Gait Analysis through Transformation-Based Multiple Linear Regression
Normalization.- Model and Threshold Selection in the Peaks-Over-Threshold
(POT) Methodology: Application to Extreme Precipitation Values in Madeira and
Porto Santo Islands.- Revisiting Estimation Methods for Some Parameters of
Rare Events.- Clustering and Classification of Compositional Data Using
Distributions Defined on the Hypersphere.- Joint Models of Longitudinal
Binary Responses: A Nonparametric Bayesian Approach.
Format: Hardback, 265 pages, height x width: 235x155 mm, 53 Illustrations, color; 57 Illustrations, black and white; Approx. 300 p.,
Series: Interdisciplinary Applied Mathematics 61
Pub. Date: 30-Dec-2024
ISBN-13: 9783031716850
Dive into the fascinating world of economic agglomerations with this interdisciplinary study, which is perfect for readers in nonlinear mathematics, economic geography, and spatial economics. This book uniquely bridges these fields, employing group-theoretic bifurcation analysis in nonlinear mathematics to establish a robust theoretical foundation for economic geographers and mathematicians alike.
Explore innovative models that describe the pattern formation in economic agglomerations through worker migration between regions. Delve into multi-regional formulations of classic economic geography models, applied to various spatial platforms such as line segments, racetracks, squares, and hexagonal lattices.
This book, ideal for researchers and practitioners, offers cutting-edge insights and methodologies for understanding the complexities of spatial economic agglomerations.
Introduction to Bifurcation Analysis in Economic Geography.
.- Introduction to Economic Agglomeration Analysis.
.- Part I Bifurcation from the Uniform State.
.- Racetrack Economy: Introduction to Group-Theoretic Analysis.
.- Group-Theoretic Analysis of Square Lattice.
.- Group-Theoretic Stability Analysis of Hexagonal Lattice.
.- Spectrum Analysis of Population Data in German Reunification.
.- Locational Heterogeneity and Catastrophe in Two-Place Economy.
.- Analysis of Break points.
.- Part II Hierarchical Bifurcations and Invariant Patterns.
.- Racetrack Economy: Hierarchical Bifurcation and Invariant Patterns.
.- Invariant Patterns on Square and Hexagonal Lattices.
.- GlobalLocal Spatial Network.
.- Spatial Period-Doubling Cascade in Long-Narrow Economy.
.- Spatial Period-Doubling Cascade on Square Lattice.
.- Equidistant Economy.