LEADER 04921nam 2200673Ia 450 001 9910462018803321 005 20211202220822.0 010 $a3-11-089135-2 024 7 $a10.1515/9783110891355 035 $a(CKB)2670000000251071 035 $a(EBL)934895 035 $a(SSID)ssj0000595053 035 $a(PQKBManifestationID)11354592 035 $a(PQKBTitleCode)TC0000595053 035 $a(PQKBWorkID)10554699 035 $a(PQKB)10846214 035 $a(MiAaPQ)EBC934895 035 $a(WaSeSS)Ind00010152 035 $a(DE-B1597)56098 035 $a(OCoLC)840444354 035 $a(OCoLC)842286424 035 $a(DE-B1597)9783110891355 035 $a(PPN)175503281 035 $a(Au-PeEL)EBL934895 035 $a(CaPaEBR)ebr10597994 035 $a(OCoLC)843204843 035 $a(EXLCZ)992670000000251071 100 $a20021003d2003 uy 0 101 0 $aeng 135 $aurnn#---|u||u 181 $ctxt 182 $cc 183 $acr 200 10$aDiscontinuous groups of isometries in the hyperbolic plane$b[electronic resource] /$fWerner Fenchel, Jakob Nielsen ; edited by Asmus L. Schmidt 210 $aBerlin ;$aNew York $cWalter de Gruyter$d2003 215 $a1 online resource (388 p.) 225 0 $aDe Gruyter studies in mathematics ;$v29 300 $aDescription based upon print version of record. 311 0 $a3-11-017526-6 320 $aIncludes bibliographical references (p. [355]-359) and index. 327 $tFront matter --$tChapter I. Möbius transformations and non-euclidean geometry. --$t§1 Pencils of circles - inversive geometry --$t§2 Cross-ratio --$t§3 Möbius transformations, direct and reversed --$t§4 Invariant points and classification of Möbius transformations --$t§5 Complex distance of two pairs of points --$t§6 Non-euclidean metric --$t§7 Isometric transformations --$t§8 Non-euclidean trigonometry --$t§9 Products and commutators of motions --$tChapter II. Discontinuous groups of motions and reversions. --$t§10 The concept of discontinuity --$t§11 Groups with invariant points or lines --$t§12 A discontinuity theorem --$t§13 ?-groups. Fundamental set and limit set --$t§14 The convex domain of an ?-group. Characteristic and isometric neighbourhood --$t§15 Quasi-compactness modulo ? and finite generation of ? --$tChapter III. Surfaces associated with discontinuous groups. --$t§16 The surfaces D modulo ? and K(?) modulo ? --$t§17 Area and type numbers --$tChapter IV. Decompositions of groups. --$t§18 Composition of groups --$t§19 Decomposition of groups --$t§20 Decompositions of ?-groups containing reflections --$t§21 Elementary groups and elementary surfaces --$t§22 Complete decomposition and normal form in the case of quasi-compactness --$t§23 Exhaustion in the case of non-quasi-compactness --$tChapter V. Isomorphism and homeomorphism. --$t§24 Topological and geometrical isomorphism --$t§25 Topological and geometrical homeomorphism --$t§26 Construction of g-mappings. Metric parameters. Congruent groups --$tSymbols and definitions --$tAlphabets --$tBibliography --$tIndex 330 $aThis is an introductory textbook on isometry groups of the hyperbolic plane. Interest in such groups dates back more than 120 years. Examples appear in number theory (modular groups and triangle groups), the theory of elliptic functions, and the theory of linear differential equations in the complex domain (giving rise to the alternative name Fuchsian groups). The current book is based on what became known as the famous Fenchel-Nielsen manuscript. Jakob Nielsen (1890-1959) started this project well before World War II, and his interest arose through his deep investigations on the topology of Riemann surfaces and from the fact that the fundamental group of a surface of genus greater than one is represented by such a discontinuous group. Werner Fenchel (1905-1988) joined the project later and overtook much of the preparation of the manuscript. The present book is special because of its very complete treatment of groups containing reversions and because it avoids the use of matrices to represent Moebius maps. This text is intended for students and researchers in the many areas of mathematics that involve the use of discontinuous groups. 410 3$aDe Gruyter Studies in Mathematics 606 $aDiscontinuous groups 606 $aIsometrics (Mathematics) 608 $aElectronic books. 615 0$aDiscontinuous groups. 615 0$aIsometrics (Mathematics) 676 $a514/.2 700 $aFenchel$b W$g(Werner),$f1905-$0492545 701 $aNielsen$b Jakob$f1890-1959.$0737717 701 $aSchmidt$b Asmus L$01053255 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910462018803321 996 $aDiscontinuous groups of isometries in the hyperbolic plane$92485070 997 $aUNINA LEADER 05635nam 22007935 450 001 9910720065303321 005 20251008135033.0 010 $a9783031248122$b(electronic bk.) 010 $z9783031248115 024 7 $a10.1007/978-3-031-24812-2 035 $a(MiAaPQ)EBC7243100 035 $a(Au-PeEL)EBL7243100 035 $a(DE-He213)978-3-031-24812-2 035 $a(OCoLC)1378935784 035 $a(PPN)269655972 035 $a(CKB)26540746300041 035 $a(EXLCZ)9926540746300041 100 $a20230429d2023 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aModeling and Optimization in Space Engineering $eNew Concepts and Approaches /$fedited by Giorgio Fasano, János D. Pintér 205 $a1st ed. 2023. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2023. 215 $a1 online resource (403 pages) 225 1 $aSpringer Optimization and Its Applications,$x1931-6836 ;$v200 311 08$aPrint version: Fasano, Giorgio Modeling and Optimization in Space Engineering Cham : Springer International Publishing AG,c2023 9783031248115 320 $aIncludes bibliographical references. 327 $aAdvances in the Control Propellant Minimization for the Next Generation Gravity Mission (A. Anselmi ) -- Transition of Two-dimensional Quasi-periodic Invariant Tori in the Real-ephemeris Model of the Earth-Moon System (N. Baresi) -- Hypersonic Point-to-Point Travel for the Common Man (E. Mooij) -- Bifocal Metrology Applications in Space Engineering (F. Bresciani) -- A Revisited Analysis of the Radioisotope Sail and its Possible Application to Relativistic Spaceflight (L. Derosa) -- The ERC-Funded EXTREMA Project: Achieving Self-Driving Interplanetary CubeSats (G. Di Domenico) -- Data Reduction for Optimizing the Attitude Control Dispatch in a Spacecraft (C. Durand) -- Second Order Suf?cient Conditions of Strong Minimality with applications to Orbital Transfers (L. Mazzini) -- Evolutionary Optimisation of a Flexible-Launcher Simple Adaptive Control System (E. Mooij) -- Optimization and Solution Approaches in Utilizing Wireless Sensor Networks for Exploring Moon Planets and Space (O. Ozkan) -- Near-Optimal Guidance and Pulse-Modulated Reduced Attitude Control for Orbit Injection (M. Pontani) -- A Pareto front numerical reconstruction strategy applied to a satellite system conceptual design (M. Sebastián) -- Indirect optimization of robust orbit transfer considering thruster underperformance (F. Simeoni) -- Time-Varying Lyapunov Control Laws with Enhanced Estimation of Distribution Algorithm for Low-Thrust Trajectory Design (R. Armellin). 330 $aThis volume consists of 14 contributed chapters written by leading experts, offering in-depth discussions of the mathematical modeling and algorithmic aspects for tackling a range of space engineering applications. This book will be of interest to researchers and practitioners working in the field of space engineering. Since it offers an in-depth exposition of the mathematical modelling, algorithmic and numerical solution aspects of the topics covered, the book will also be useful to aerospace engineering graduates and post-graduate students who wish to expand their knowledge by studying real-world applications and challenges that they will encounter in their profession. Readers will obtain a broad overview of some of the most challenging space engineering operational scenarios of today and tomorrow: this will be useful for managers in the aerospace field, as well as in other industrial sectors. The contributed chapters are mainly focused on space engineering practice. Researchers andpractitioners in mathematical systems modelling, operations research, optimization, and optimal control will also benefit from the case studies presented in this book. The model development and optimization approaches discussed can be extended towards other application areas that are not directly related to space engineering. Therefore, the book can be a useful reference to assist in the development of new modelling and optimization applications. 410 0$aSpringer Optimization and Its Applications,$x1931-6836 ;$v200 606 $aMathematical optimization 606 $aCalculus of variations 606 $aAerospace engineering 606 $aAstronautics 606 $aArtificial intelligence 606 $aOperations research 606 $aManagement science 606 $aDynamics 606 $aCalculus of Variations and Optimization 606 $aAerospace Technology and Astronautics 606 $aArtificial Intelligence 606 $aOperations Research, Management Science 606 $aDynamical Systems 615 0$aMathematical optimization. 615 0$aCalculus of variations. 615 0$aAerospace engineering. 615 0$aAstronautics. 615 0$aArtificial intelligence. 615 0$aOperations research. 615 0$aManagement science. 615 0$aDynamics. 615 14$aCalculus of Variations and Optimization. 615 24$aAerospace Technology and Astronautics. 615 24$aArtificial Intelligence. 615 24$aOperations Research, Management Science. 615 24$aDynamical Systems. 676 $a629.4 676 $a629.4015196 702 $aFasano$b Giorgio 702 $aPinte?r$b J. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910720065303321 996 $aModeling and Optimization in Space Engineering$91732590 997 $aUNINA