Free Download Category and Measure: Infinite Combinatorics, Topology and Groups
English | 2025 | ISBN: 0521196078 | 347 Pages | PDF | 5.4 MB
Topological spaces in general, and the real numbers in particular, have the characteristic of exhibiting a ‘continuity structure’, one that can be examined from the vantage point of Baire category or of Lebesgue measure. Though they are in some sense dual, work over the last half-century has shown that it is the former, topological view, that has pride of place since it reveals a much richer structure that draws from, and gives back to, areas such as analytic sets, infinite games, probability, infinite combinatorics, descriptive set theory and topology. Keeping prerequisites to a minimum, the authors provide a new exposition and synthesis of the extensive mathematical theory needed to understand the subject’s current state of knowledge, and they complement their presentation with a thorough bibliography of source material and pointers to further work. The result is a book that will be the standard reference for all researchers in the area.

Free Download Efficient Topology Estimation for Large Scale Optical Mapping By Armagan Elibol, Nuno Gracias, Rafael Garcia (auth.)
2013 | 88 Pages | ISBN: 3642303129 | PDF | 8 MB
Large scale optical mapping methods are in great demand among scientists who study different aspects of the seabed, and have been fostered by impressive advances in the capabilities of underwater robots in gathering optical data from the seafloor. Cost and weight constraints mean that low-cost ROVs usually have a very limited number of sensors. When a low-cost robot carries out a seafloor survey using a down-looking camera, it usually follows a predefined trajectory that provides several non time-consecutive overlapping image pairs. Finding these pairs (a process known as topology estimation) is indispensable to obtaining globally consistent mosaics and accurate trajectory estimates, which are necessary for a global view of the surveyed area, especially when optical sensors are the only data source. This book contributes to the state-of-art in large area image mosaicing methods for underwater surveys using low-cost vehicles equipped with a very limited sensor suite. The main focus has been on global alignment and fast topology estimation, which are the most challenging steps in creating large area image mosaics. This book is intended to emphasise the importance of the topology estimation problem and to present different solutions using interdisciplinary approaches opening a way to further develop new strategies and methodologies.

Free Download Effective Non-Hermiticity and Topology in Markovian Quadratic Bosonic Dynamics (Springer Theses) by Vincent Paul Flynn
English | April 19, 2024 | ISBN: 3031520440 | 259 pages | MOBI | 28 Mb
This thesis provides an in-depth investigation of effective non-Hermiticity and topology in many-mode, non-interacting, bosonic systems. It also establishes the extent to which one must move beyond the Hamiltonian, closed-system setting, in order to uncover signatures of genuine symmetry-protected topological (SPT) physics in "free" (mean-field) bosons. While SPT phases of free fermionic matter and their associated zero-energy boundary-localized modes have been thoroughly explored, similar physics in free bosonic systems still remains elusive. No fermionic counterpart exists for the distinctive dynamical behavior that arises from the effective non-Hermiticity, intrinsic even at equilibrium, to bosonic Hamiltonians. Therefore, a much needed paradigm shift is required to address major conceptual roadblocks in the search for SPT bosonic phases.

Free Download N. Bourbaki, "General Topology: Chapters 1-4"
English | 1995 | pages: 443 | ISBN: 3540642412, 354019374X | PDF | 39,9 mb
This is the softcover reprint of the English translation of 1971 (available from Springer since 1989) of the first 4 chapters of Bourbaki’s Topologie générale. It gives all the basics of the subject, starting from definitions. Important classes of topological spaces are studied, uniform structures are introduced and applied to topological groups. Real numbers are constructed and their properties established. Part II, comprising the later chapters, Ch. 5-10, is also available in English in softcover.

Free Download Elementza – Hard Surface Topology Workshop

elementza | Duration: 15 h | Video: H264 2560×1440 | Audio: AAC 48 kHz 2ch | 7,23 GB | Language: English
In this course, we´ll:
• cover variety of examples with different approaches, and discuss which ones bring the cleanest and production friendly results.
• cover multiple examples with variety of approaches once more, and discuss the results. We´ll try out boolean workflow, we´ll do topology cleanup, but also try more natural workflow where topology sets the rules for the shapes.

Free Download Topology of Superconductors:
Theory of Symmetry Indicators, Classifications of Superconducting Nodes, and High-Throughput Investigations
English | 2024 | ISBN: 9819773989 | 139 Pages | PDF EPUB (True) | 17 MB

Free Download Symmetries, Topology and Resonances in Hamiltonian Mechanics By Valerij V. Kozlov (auth.)
1996 | 378 Pages | ISBN: 3642783953 | PDF | 11 MB
John Hornstein has written about the author’s theorem on nonintegrability of geodesic flows on closed surfaces of genus greater than one: "Here is an example of how differential geometry, differential and algebraic topology, and Newton’s laws make music together" (Amer. Math. Monthly, November 1989). Kozlov’s book is a systematic introduction to the problem of exact integration of equations of dynamics. The key to the solution is to find nontrivial symmetries of Hamiltonian systems. After Poincaré’s work it became clear that topological considerations and the analysis of resonance phenomena play a crucial role in the problem on the existence of symmetry fields and nontrivial conservation laws.

Free Download Geometry, Topology and Quantization By Pratul Bandyopadhyay (auth.)
1996 | 230 Pages | ISBN: 940106282X | PDF | 19 MB
This is a monograph on geometrical and topological features which arise in various quantization procedures. Quantization schemes consider the feasibility of arriving at a quantum system from a classical one and these involve three major procedures viz. i) geometric quantization, ii) Klauder quantization, and iii) stochastic quanti zation. In geometric quantization we have to incorporate a hermitian line bundle to effectively generate the quantum Hamiltonian operator from a classical Hamil tonian. Klauder quantization also takes into account the role of the connection one-form along with coordinate independence. In stochastic quantization as pro posed by Nelson, Schrodinger equation is derived from Brownian motion processes; however, we have difficulty in its relativistic generalization. It has been pointed out by several authors that this may be circumvented by formulating a new geometry where Brownian motion proceses are considered in external as well as in internal space and, when the complexified space-time is considered, the usual path integral formulation is achieved. When this internal space variable is considered as a direc tion vector introducing an anisotropy in the internal space, we have the quantization of a Fermi field. This helps us to formulate a stochastic phase space formalism when the internal extension can be treated as a gauge theoretic extension. This suggests that massive fermions may be considered as Skyrme solitons. The nonrelativistic quantum mechanics is achieved in the sharp point limit.

Free Download . Andima, "General Topology and Applications"
English | 1991 | pages: 437 | ISBN: 0824785525 | PDF | 17,0 mb
This book is based on the proceedings of the Fifth Northeast Conference on General Topology and Applications, held at The College of Staten Island – The City University of New York. It provides insight into the relationship between general topology and other areas of mathematics.

Free Download Geometry and Topology of Low Dimensional Systems: Chern-Simons Theory with Applications by T. R. Govindarajan , Pichai Ramadevi
English | PDF EPUB (True) | 2024 | 174 Pages | ISBN : 3031595009 | 13.6 MB