Knots / / Gerhard Burde, Heiner Zieschang, Michael Heusener

• Record Nr.: UNINA9910453774803321
• Autore: Burde Gerhard <1931->
• Pubbl/distr/stampa: Berlin ; ; Boston : , : Walter de Gruyter GmbH & Co. KG, , 2013
• ISBN: 3-11-027078-1
• Edizione: [Third, fully revised and extended edition.]
• Descrizione fisica: 1 online resource (432 p.)
• Collana: De Gruyter Studies in Mathematics ; ; 5; De Gruyter studies in mathematics, , 0179-0986 ; ; 5
• Altri autori (Persone): ZieschangHeiner; HeusenerMichael
• Disciplina: 514/.2242
• Soggetti: Knot theory; Electronic books.
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and indexes.
• Nota di contenuto: Frontmatter -- Preface to the First Edition -- Preface to the Second Edition -- Preface to the Third Edition -- Contents -- Chapter 1: Knots and isotopies -- Chapter 2: Geometric concepts -- Chapter 3: Knot groups -- Chapter 4: Commutator subgroup of a knot group -- Chapter 5: Fibered knots -- Chapter 6: A characterization of torus knots -- Chapter 7: Factorization of knots -- Chapter 8: Cyclic coverings and Alexander invariants -- Chapter 9: Free differential calculus and Alexander matrices -- Chapter 10: Braids -- Chapter 11: Manifolds as branched coverings -- Chapter 12: Montesinos links -- Chapter 13: Quadratic forms of a knot -- Chapter 14: Representations of knot groups -- Chapter 15: Knots, knot manifolds, and knot groups -- Chapter 16: Bridge number and companionship -- Chapter 17: The 2-variable skein polynomial -- Appendix A: Algebraic theorems -- Appendix B: Theorems of 3-dimensional topology -- Appendix C: Table -- Appendix D: Knot projections 01-949 -- References -- Author index -- Glossary of Symbols -- Index
• Sommario/riassunto: This book is an introduction to classical knot theory. Topics covered include: different constructions of knots, knot diagrams, knot groups, fibred knots, characterisation of torus knots, prime decomposition of knots, cyclic coverings and Alexander polynomials and modules together with the free differential calculus, braids, branched coverings ; and knots, Montesinos links, representations of knot groups, surgery of 3-manifolds and knots, Jones and HOMFLYPT polynomials. Knot theory has expanded enormously since the first edition of this book published in 1985. In this third completely revised and extended edition a chapter about bridge number and companionship of knots has been added. The book contains many figures and some tables of invariants of knots. This comprehensive account is an indispensable reference source for anyone interested in both classical and modern knot theory. Most of the topics considered in the book are developed in detail; only the main properties of fundamental groups, covering spaces and some basic results of combinatorial group theory are assumed to be known. The text is accessible to advanced undergraduate and graduate students in mathematics.

Solar-Terrestrial Relations and Physics of Earthquake Precursors : Proceedings of the XIII International Conference / / Alexei Dmitriev [and three others], editors

• Record Nr.: UNINA9910799217303321
• Pubbl/distr/stampa: Cham, Switzerland : , : Springer, , [2023]; ©2023
• ISBN: 3-031-50248-5
• Edizione: [First edition.]
• Descrizione fisica: 1 online resource (301 pages)
• Collana: Springer Proceedings in Earth and Environmental Sciences Series
• Disciplina: 538.76
• Soggetti: Solar-terrestrial physics
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Intro -- Preface -- Organization -- Contents -- Atmosphere Physics -- Analysis of Ionospheric Parameters During Solar Events and Magnetic Storms -- 1 Introduction -- 2 Generalized Multicomponent Model of Ionospheric Parameters and a Method for Detecting Ionospheric Disturbances -- 2.1 Regular Component of the Model and a Method for Detecting Intense Ionospheric Disturbances -- 2.2 Anomalous Component of the Model and a Method for Detecting Shot-Period ; Ionospheric Disturbances -- 3 Experimental Results and Discussion -- 4 Conclusions -- References -- Estimation of Characteristics of Atmospheric Ionization Rates Taking into Account Different Energies of Precipitating Electrons -- 1 Introduction -- 2 Ionization Rates Taking into Account Electrons with Initial Energy from Several of keV Up to Several MeV -- 3 Conclusions -- References -- Dust Plasma in the Region of Active Influence on the Ionosphere -- 1 Introduction -- 2 Method -- 3 Results -- 4 Concluding Remarks -- References -- Ozone Dynamics During Geomagnetic and Meteorological Disturbances in October 2015 and 2018 -- 1 Introduction -- 2 Data and Selections of Event -- 3 Ozone in the Mesosphere and Lower Thermosphere -- 4 Discussion -- 5 Conclusion -- References -- Observations of the Meteoric Aerosol in the Stratosphere Above Tomsk in August 2013 -- 1 Introduction -- 2 Experimental Data and the Procedure of Trajectory Analysis -- 3 Results of the Lidar Observations of Aerosol Above Tomsk in August 2013 -- 4 Results of Trajectory Analysis Involving the Satellite Data -- 5 Conclusion -- References -- Impact of Solar Activity on the Optical Properties of the Thermosphere -- 1 Introduction -- 2 Glow Spectra of the Night Sky -- 3 Discussion -- 4 Conclusion -- References -- Relation Between Sprites and Whistlers Based on AWDANET and WWLLN Data -- 1 Introduction.; 2 Atmospherics Initiated by Sprites -- 3 Whistlers and Sprites -- 4 Conclusions -- References -- Analysis of Electromagnetic Radiation During Shiveluch and Bezymyanniy Volcano Eruptions from 2017 to 2023 -- 1 Introduction -- 2 Instrumentation and Observation Method -- 3 Analysis of Electromagnetic Radiation During Shiveluch and Bezymianniy Volcano Eruptions -- 3.1 Examples of Records of Lightning Strokes Accompanying Explosive Eruptions of Kamchatka Volcanos Until 2022 -- 3.2 Mechanism of Lightning Formation in Eruptive Clouds -- 3.3 Remote Methods for Observations of Shiveluch and Bezymianniy Volcano Eruptions in April 2023 -- 4 Conclusions -- References -- Space Project ``Modulation'', a New Approach to Studying the Fluxes of Galactic Cosmic Rays in the Field of Solar Modulation Energies -- 1 Introduction -- 2 Methodology for Registration of Nuclei from Protons to Iron in the MODULATION Project -- 2.1 Instrument Design -- 2.2 Mathematical Modelling of the Spectrometer -- 2.3 Full Energy Absorption Mode. Minimum and Maximum Energy Thresholds of the Full Absorption Mode -- 2.4 Full Ionisation Loss Method in the Incomplete Energy Absorption Regime -- 3 MODULATION Spectrometer Design Image -- 4 Conclusion -- References -- Geophysical Fields and Their Interaction -- Geomagnetic Measurements at the Pleshchenitsy Geophysical Observatory (Minsk, Republic of Belarus) -- 1 Introduction -- 2 Historical Investigations of the Earth's Magnetic Field in Belarus -- 3 Description of the Pleshchenitsy Geophysical Observatory -- 4 Observations of the Geomagnetic Field Elements at the Pleshchenitsy Geophysical Observatory -- 5 Analysis of the Geomagnetic Field Disturbance Carried Out at the Pleshchenitsy Geophysical Observatory -- 6 Conclusions -- References -- Advanced Instruments for Geo and Helio Environment Monitoring on the Cubesat Format Spacecraft.; 1 Introduction -- 2 Instruments for Radiation Monitoring on Cubesats -- 2.1 The DeCoR Instrument -- 2.2 The KODIZ Instrument -- 3 Examples of Radiation Measurements with DeCoR Instruments -- 4 Next-generation Space Radiation Detectors for Nanosatellites -- 5 Conclusion -- References -- Oscillator Associated with One Two-Mode Dynamo Model with Memory -- 1 Introduction -- 2 Two-Modes -Dynamo with Memory as Hereditary Oscillator -- 3 Simulation Results -- 3.1 Instant -Quenching: K(r)=exp(-r) -- 3.2 Delay of -Quenching: K; (r)=rexp(-r) -- 4 Discussion -- References -- Atmosphere and Lithosphere Interaction Could Triggered the 2023 Mw 7.8 Turkey Earthquake -- 1 Introduction -- 2 Earthquakes and Tropical Cyclones Interrelation Background -- 3 Analysis of the 2022-2023 Tropical Cyclogenesis Preceding the 2023 Mw 7.8 Turkey Earthquake -- 4 Tilt-Baric and Strain-Baric Processes Preceding and Accompanying the 2023 Mw 7.8 Turkey Earthquake -- 5 Conclusion -- References -- Analysis of Cosmic Ray Variations During Geomagnetic Storms in 2019-2022 -- 1 Introduction -- 2 Description of the Methods -- 2.1 Singular Spectrum Analysis -- 2.2 Adaptive Algorithm for Anomaly Detection -- 3 Results of Data Processing -- 4 Conclusions -- References -- Analysis of Ionospheric Parameters Based on Threshold Wavelet Filtering (from foF2 Data of Paratunka (Russia) and Wakkanai (Japan) Stations) -- 1 Introduction -- 2 Method Description -- 3 Results of the Method Application -- 4 Analysis of Results and Conclusions -- References -- Seismoacoustic and Seismoelectric Responses of Near-Surface Sedimentary Rocks in Kamchatka -- 1 Relevance of Research -- 2 Observation Method and Data Analysis -- 3 Seismoacoustic and Seismoelectric Responses of Rocks at Karymshina Site -- 4 High-Frequency Seismoacoustic Responses of Rocks at Krutoberegovo Site -- 5 Conclusions -- References.; Monitoring of Radiation Fields in Near-Earth Space with the Use of Kodiz Instrument On-Board Cubesat Monitor-1 -- 1 Introduction -- 2 KODIZ Design -- 2.1 Detectors of the Device KODIZ -- 2.2 Digital Signal Processing Unit -- 3 Results -- 3.1 Evaluation of the Performance of the KODIZ Device in Flight Conditions -- 4 Conclusion -- References -- Selkov Dynamic System with Variable Heredity for Describing Microseismic Regimes -- 1 Introduction -- 2 Problem Statement and Solution Technique -- 3 Results -- 4 Conclusion -- References -- Variations in the Parameters of the Signal from the A1F3 VLF Transmitter Received at the Mikhnevo Geophysical Observatory During a Series of Earthquakes in Turkey in February 2023 -- 1 Introduction -- 2 Results -- 3 Discussion and Conclusions -- References -- SME Geomagnetic Index Data Forecast Based on Wavelet Transform and LSTM Neural Networks -- 1 Introduction -- 2 Methodology -- 3 Experimental Results -- 4 Conclusions -- References -- Observations of Space Weather Effects from the Moscow University Nano-satellite Constellation Sozvezdie-270 -- 1 Introduction -- 2 Multi-satellite Mission of Moscow University -- 2.1 Scientific and Educational Experiments On-Board Cubesats -- 2.2 The Project "Constellation-270" -- 3 Results of Space Weather Effects Observations with the Use of Cubesats -- 3.1 Solar Cosmic Ray Effects in Near-Earth Space -- 3.2 The Outer Radiation Belt Dynamics During the Magnetic Storm -- 4 Conclusion -- References -- Matching the Parameters of Shell Turbulence Models with the Probabilities of Interaction of Wave Shells -- 1 Introduction -- 2 Building Shell Models -- 3 Invariants -- 4 Spectral Laws -- 5 Probabilities of Interaction -- 6 Computational Experiments -- 7 Discussion -- References -- About Some Small Effects in Magnetic Field at Observatories Paratunka (Kamchatka, Russia) and Choutuppal (India).; 1 Introduction -- 2 Local Effects in the Magnetic Field at the Observatory Paratunka -- 2.1 Spatial Gradient of the Total Field Intensity in the Pavilion for Absolute Observations -- 2.2 Variations of the Magnetic Field in the dIdD Magnetometer Pavilion -- 2.3 Possible Interpretations of Small Magnetic Effects at the Observatory Paratunka -- 3 About Some Small Effects in Magnetic Field at Low Latitude Observatory Choutuppal, India -- 4 Discussion -- 5 Conclusion -- References -- Conditions for Generating a Chaotic Regime in a Low-; Mode -Dynamo Model with Hereditary -Quenching by Field Energy -- 1 Introduction -- 2 Stability Conditions of the Solution According to Lyapunov -- 3 Discussion -- 4 Conclusion -- References -- Physics of Earthquake Precursors -- Disturbances in E and F Layers of the Ionosphere Preceding Earthquakes in the Kamchatka Region -- 1 Introduction -- 2 Data Analysis Methodology -- 3 Results of the Analysis of the Predictive Efficiency of Ionospheric Parameters -- 4 Conclusions -- References -- Nonextensive Analysis of Natural and Technogenic Seismicity of Sakhalin Island -- 1 Introduction -- 2 Initial Data -- 3 Methods -- 4 Results and Discussion -- 5 Conclusion -- References -- Power-Law Compound and Fractional Poisson Process in the Theory of Anomalous Phenomena -- 1 Introduction -- 2 Compound Fractional Poisson Process -- 3 Series of Repeatability Frequencies of Events -- 4 Critical Indexes and Process Instability -- 5 Analysis of Seismic Data -- 5.1 Determination of the Parameters of the Distribution of Repeatability Frequencies -- 5.2 Distributions of the First-Passage Times -- 5.3 Results -- 6 Discussion -- 7 Conclusion -- References -- Operational Precursors of the Earthquake on March 16, 2021 with Mw = 6.6, Kamchatka -- References -- Author Index.