Format: Paperback / softback,
261 pages, height x width: 235x155 mm,
47 Illustrations, black and white; XVII, 261 p. 47 illus
Series: La Matematica per il 3+2 134
Pub. Date: 15-Jun-2022
ISBN-13: 9789811694837
This book starts with a discussion of the classical intermediate value theorem and some of its uncommon “topological” consequences as an appetizer to whet the interest of the reader. It is a concise introduction to topology with a tinge of historical perspective, as the author’s perception is that learning mathematics should be spiced up with a dash of historical development. All the basics of general topology that a student of mathematics would need are discussed, and glimpses of the beginnings of algebraic and combinatorial methods in topology are provided.
All the standard material on basic set topology is presented, with the treatment being sometimes new. This is followed by some of the classical, important topological results on Euclidean spaces (the higher-dimensional intermediate value theorem of Poincare?Miranda, Brouwer’s fixed-point theorem, the no-retract theorem, theorems on invariance of domain and dimension, Borsuk’s antipodal theorem, the Borsuk?Ulam theorem and the Lusternik?Schnirelmann?Borsuk theorem), all proved by combinatorial methods. This material is not usually found in introductory books on topology. The book concludes with an introduction to homotopy, fundamental groups and covering spaces.
Throughout, original formulations of concepts and major results are provided, along with English translations. Brief accounts of historical developments and biographical sketches of the dramatis personae are provided. Problem solving being an indispensable process of learning, plenty of exercises are provided to hone the reader's mathematical skills. The book would be suitable for a first course in topology and also as a source for self-study for someone desirous of learning the subject. Familiarity with elementary real analysis and some felicity with the language of set theory and abstract mathematical reasoning would be adequate prerequisites for an intelligent study of the book.
1 Aperitif: The Intermediate Value Theorem.- 2 Metric spaces.- 3 Topological spaces.- 4 Continuous maps.- 5 Compact spaces.- 6Topologies defined by maps.- 7 Products of compact spaces.- 8 Separation axioms.- 9 Connected spaces.- 10 Countability axioms.
Format: Paperback / softback,
337 pages, height x width: 235x155 mm,
1 Illustrations, color; 53 Illustrations, black and white; XVII, 337 p. 54 illus., 1 illus. in color.
Series: UNITEXT 136
Pub. Date: 05-Jun-2022
ISBN-13: 9789811904967
This textbook expounds the major topics in the special theory of relativity. It provides a detailed examination of the mathematical foundation of the special theory of relativity, relativistic mass, relativistic mechanics, and relativistic electrodynamics. As well as covariant formulation of relativistic mechanics and electrodynamics, the text discusses the relativistic effect on photons. A new chapter on electromagnetic waves as well as several new problems and examples have been included in the second edition of the book. Using the mathematical approach, the text offers graduate students a clear, concise view of the special theory of relativity. Organized into 15 chapters and two appendices, the content is presented in a logical order, and every topic has been dealt with in a simple and lucid manner. To aid understanding of the subject, the text provides numerous relevant worked-out examples in every chapter. The mathematical approach of the text helps students in their independent study and motivates them to research the topic further.
Pre-Relativity and Galilean Transformations.- Michelson-Morley Experiment and Velocity of Light.- Lorentz Transformations.- Mathematical Properties of Lorentz Transformations.- More mathematical Properties of Lorentz Transformations.- Geometrical Interpretation of spacetime.- Relativistic Velocity and Acceleration.- Four Dimensional World.- Mass in Relativity.- Relativistic Dynamics.- Photon in Relativity.- Relativistic Lagrangian and Hamiltonian.- Electrodynamics in Relativity.- Electromagnetic waves.- Relativistic Mechanics of Continua.
Format: Paperback / softback,
239 pages, height x width: 235x155 mm, XII, 239 p.,
Series: Lecture Notes in Mathematics 2298
Pub. Date: 10-Jun-2022
ISBN-13: 9783030964320
This book reviews the theory of 'generalized B*-algebras' (GB*-algebras), a class of complete locally convex *-algebras which includes all C*-algebras and some of their extensions. A functional calculus and a spectral theory for GB*-algebras is presented, together with results such as Ogasawara's commutativity condition, Gelfand?Naimark type theorems, a Vidav?Palmer type theorem, an unbounded representation theory, and miscellaneous applications.
Numerous contributions to the subject have been made since its initiation by G.R. Allan in 1967, including the notable early work of his student P.G. Dixon. Providing an exposition of existing research in the field, the book aims to make this growing theory as familiar as possible to postgraduate students interested in functional analysis, (unbounded) operator theory and its relationship to mathematical physics. It also addresses researchers interested in extensions of the celebrated theory of C*-algebras.
Contents.- Introduction.-
1. A Spectral Theory for Locally Convex Algebras.-
2. Generalized B*-Algebras: Functional Representation Theory.-
3. Commutative Generalized B*-Algebras: Functional Calculus and Equivalent Topologies.-
4. Extended C*-Algebras and Extended W*-Algebras.-
5. Generalized B*-Algebras: Unbounded *-Representation Theory.-
6. Applications I: Miscellanea.- 7 Applications II: Tensor Products.- Bibliograpy.- Index.
Format: Paperback / softback,
170 pages, height x width: 235x155 mm,
4 Illustrations, black and white; X, 170 p. 4 illus
Series: Lecture Notes in Mathematics 2299
Pub. Date: 03-Jun-2022
ISBN-13: 9789811910951
The present monograph further develops the study, via the techniques of combinatorial anabelian geometry, of the profinite fundamental groups of configuration spaces associated to hyperbolic curves over algebraically closed fields of characteristic zero.
The starting point of the theory of the present monograph is a combinatorial anabelian result which allows one to reduce issues concerning the anabelian geometry of configuration spaces to issues concerning the anabelian geometry of hyperbolic curves, as well as to give purely group-theoretic characterizations of the cuspidal inertia subgroups of one-dimensional subquotients of the profinite fundamental group of a configuration space.
We then turn to the study of tripod synchronization, i.e., of the phenomenon that an outer automorphism of the profinite fundamental group of a log configuration space associated to a stable log curve induces the same outer automorphism on certain subquotients of such a fundamental group determined by tripods [ i.e., copies of the projective line minus three points]. The theory of tripod synchronization shows that such outer automorphisms exhibit somewhat different behavior from the behavior that occurs in the case of discrete fundamental groups and, moreover, may be applied to obtain various strong results concerning profinite Dehn multi-twists.
In the final portion of the monograph, we develop a theory of localizability, on the dual graph of a stable log curve, for the condition that an outer automorphism of the profinite fundamental group of the stable log curve lift to an outer automorphism of the profinite fundamental group of a corresponding log configuration space. This localizability is combined with the theory of tripod synchronization to construct a purely combinatorial analogue of the natural outer surjection from the etale fundamental group of the moduli stack of hyperbolic curves over the field of rational numbers to the absolute Galois group of the field of rational numbers.
1. Combinatorial Anabelian Geometry in the Absence of Group-theoretic Cuspidality.-
2. Partial Combinatorial Cuspidalization for F-admissible Outomorphisms.-
3. Synchronization of Tripods.-
4. Glueability of Combinatorial Cuspidalizations. References.
Format: Paperback / softback,
350 pages, height x width: 235x155 mm,
2 Illustrations, black and white; X, 350 p. 2 illus.
Series: Seminaire de Probabilites 2301
Pub. Date: 16-May-2022
ISBN-13: 9783030964085
This volume presents a selection of texts that reflects the current research streams in probability, with an interest toward topics such as filtrations, Markov processes and Markov chains as well as large deviations, Stochastic Partial Differential equations, rough paths theory, quantum probabilities and percolation on graphs.
The featured contributors are R. L. Karandikar and B. V. Rao,
C. Leuridan, M. Vidmar, L. Miclo and P. Patie, A. Bernou,
M.-E. Caballero and A. Rouault, J. Dedecker, F. Merlevede and
E. Rio, F. Brosset, T. Klein, A. Lagnoux and P. Petit, C. Marinelli
and L. Scarpa, C. Castaing, N. Marie and P. Raynaud de Fitte,
S. Attal, J. Deschamps and C. Pellegrini, and N. Eisenbaum.
Stochastic Integrals and Two Filtrations.- Filtrations associated to some two-to-one transformations.- Exit problems for positive Markov processes with one-sided jumps.- On intertwining relations between Ehrenfest, Yule and Ornstein-Uhlenbeck processes.- On subexponential convergence to equilibrium of Markov processes.- Invariance principle for clocks.- Criteria for Borel-Cantelli lemmas with applications to Markov chains and dynamical systems.- Probabilistic proofs of large deviation results for sums of semiexponential random variables and explicit rate function at the transition.- Well-posedness of monotone semilinear SPDEs with semimartingale noise.- Sweeping processes perturbed by rough signals.- Classical Noises Emerging from Quantum Environments.- Percolation of repulsive particles on graphs.
Format: Paperback / softback,
240 pages, height x width: 235x155 mm, X, 240 p
Series: Lecture Notes in Mathematics 2304
Pub. Date: 12-Jun-2022
ISBN-13: 9783030990107
This book on recent research in noncommutative harmonic analysis treats the Lp boundedness of Riesz transforms associated with Markovian semigroups of either Fourier multipliers on non-abelian groups or Schur multipliers. The detailed study of these objects is then continued with a proof of the boundedness of the holomorphic functional calculus for Hodge?Dirac operators, thereby answering a question of Junge, Mei and Parcet, and presenting a new functional analytic approach which makes it possible to further explore the connection with noncommutative geometry. These Lp operations are then shown to yield new examples of quantum compact metric spaces and spectral triples.
The theory described in this book has at its foundation one of the great discoveries in analysis of the twentieth century: the continuity of the Hilbert and Riesz transforms on Lp. In the works of Lust-Piquard (1998) and Junge, Mei and Parcet (2018), it became apparent that these Lp operations can be formulated on Lp spaces associated with groups. Continuing these lines of research, the book provides a self-contained introduction to the requisite noncommutative background.
Covering an active and exciting topic which has numerous connections with recent developments in noncommutative harmonic analysis, the book will be of interest both to experts in no-commutative Lp spaces and analysts interested in the construction of Riesz transforms and Hodge?Dirac operators.
1. Introduction.-
2. Preliminaries.-
3. Riesz transforms associated to semigroups of Markov multipliers.-
4. Boundedness of H1 functional calculus of Hodge-Dirac operators.-
5. Locally compact quantum metric spaces and spectral triples.-
6. Appendix : Lvy measures and 1-cohomology.
Format: Paperback / softback,
height x width: 203x127 mm, Approx. 125 p
Pub. Date: 07-Jul-2022
ISBN-13: 9783662650073
What is the phenomenon of quantum entanglement? If you read popular science literature, there is talk of socks that are red and blue at the same time, but monochromatic - how is that supposed to work? If you read scientific literature, you have to have knowledge of functional analysis.
This book vividly builds the bridge between the experiments that led to quantum entanglement and the algorithm for teleportation, assuming only an elementary knowledge of mathematics.
Table of Contents
Quantum entanglement.- Concept of experiments.- Explanation by quantum physics.- Bell's inequality-there are no hidden variables.- Quantum gates.- The algorithm for teleportation.- Outlook quantum computing.