LEADER 04196nam 2200613 450 001 9910788758403321 005 20180731044137.0 010 $a1-4704-0140-1 035 $a(CKB)3360000000464745 035 $a(EBL)3113846 035 $a(SSID)ssj0000889285 035 $a(PQKBManifestationID)11488400 035 $a(PQKBTitleCode)TC0000889285 035 $a(PQKBWorkID)10876376 035 $a(PQKB)10237412 035 $a(MiAaPQ)EBC3113846 035 $a(RPAM)2559333 035 $a(PPN)195414438 035 $a(EXLCZ)993360000000464745 100 $a20140904h19951995 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aTwo-generator discrete subgroups of PSL (2, R) /$fJane Gilman 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d1995. 210 4$dİ1995 215 $a1 online resource (221 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vVolume 117, Number 561 300 $a"September 1995, volume 117, number 561 (fourth of 5 numbers)." 311 $a0-8218-0361-1 320 $aIncludes bibliographical references. 327 $a""Contents""; ""I: Introduction""; ""1 Introduction""; ""1.1 Overview Intersecting Axes""; ""1.2 Overview of the intertwining cases""; ""1.3 Why an algorithm is needed""; ""2 The Acute Triangle Theorem""; ""2.1 Nielsen equivalence""; ""2.2 Idea of proof: Acute triangle theorem""; ""2.3 Labeling Conventions""; ""2.4 Ascending order conventions""; ""2.5 The Triangle Algorithm""; ""2.6 Q and the last triangle along A""; ""2.7 Combining triangle algorithm steps""; ""2.8 The sides and heights converge to 0""; ""2.9 Acute triangle theorem: proof""; ""3 Discreteness Theorem Proof Outline"" 327 $a""3.1 The Discreteness Theorem""""3.2 Discreteness theorem""; ""3.3 Geometric equivalence theorems""; ""II: Preliminaries""; ""4 Triangle Groups and their Tilings""; ""4.1 Basic facts about triangle groups""; ""4.2 Minimal tiling distances""; ""4.3 The wedge at a vertex""; ""4.4 Proofs of lemmas and theorems""; ""4.5 Additional Notation""; ""4.6 Distances in the extended wedge""; ""5 Pentagons""; ""5.1 Constructing the pentagon, P[sub(A,B)]""; ""5.2 Notation""; ""5.3 Applying the Poincare Polygon Theorem""; ""5.4 Pentagon Tilings""; ""5.5 Distances in the shingling"" 327 $a""8.4 Pentagon distances (2,3, n) t = 3 k = 3""; ""9 Nielsen Eq: (2,3, n) t = 3; k = 3""; ""9.1 Introduction""; ""9.2 Types of triples: distances""; ""9.3 Locating t[sub(2)] and t[sub(3)]""; ""10 Nielsen Eq: (2,4, n) t = 2; k = 2""; ""10.1 Introduction""; ""10.2 Types of triples""; ""10.3 Location of t[sub(1)],t[sub(2)] and t[sub(3)]""; ""11 Pentagon t = 9 & 2a???2 Spectrum""; ""11.1 Step 1: Label the wedge""; ""11.2 Step 2: Double and Extend""; ""11.3 Step 3: Drop perpendiculars""; ""11.4 The twoa???two spectrum""; ""11.5 More distance computations""; ""11.6 Distances to qA??[sub(0)]"" 327 $a""11.7 Locate three order two points""""12 The Seven & Geometric Eq t = 9""; ""12.1 Introduction""; ""12.2 The variation of h and b""; ""12.3 Rule out a seven on the I?² side""; ""12.4 Rule out a seven on the D side""; ""12.5 Interior sevens""; ""12.6 Notation""; ""12.7 Geometric equivalence (2,3, 7) t = 9; k = 2""; ""13 Discreteness Theorem Proof""; ""13.1 The Proof of the Discreteness Theorem""; ""13.2 The proof of sufficiency""; ""IV: The Real Number Algorithm and the Turing Machine Algorithm""; ""14 Forms of the Algorithm""; ""14.1 What is an algorithm?"" 327 $a""14.2 The Elliptic Order Algorithm"" 410 0$aMemoirs of the American Mathematical Society ;$vVolume 117, Number 561. 606 $aFuchsian groups 606 $aKleinian groups 606 $aTeichmu?ller spaces 615 0$aFuchsian groups. 615 0$aKleinian groups. 615 0$aTeichmu?ller spaces. 676 $a515/.223 700 $aGilman$b Jane$f1945-$01521095 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910788758403321 996 $aTwo-generator discrete subgroups of PSL (2, R)$93760005 997 $aUNINA LEADER 03890nam 22006735 450 001 9910506376103321 005 20251225173527.0 010 $a3-030-89247-6 024 7 $a10.1007/978-3-030-89247-0 035 $a(CKB)4950000000281755 035 $a(MiAaPQ)EBC6784269 035 $a(Au-PeEL)EBL6784269 035 $a(OCoLC)1281960537 035 $a(PPN)258296372 035 $a(BIP)81914094 035 $a(BIP)81554092 035 $a(DE-He213)978-3-030-89247-0 035 $a(EXLCZ)994950000000281755 100 $a20211016d2021 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aFundamentals of Software Engineering $e9th International Conference, FSEN 2021, Virtual Event, May 19?21, 2021, Revised Selected Papers /$fedited by Hossein Hojjat, Mieke Massink 205 $a1st ed. 2021. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2021. 215 $a1 online resource (235 pages) 225 1 $aProgramming and Software Engineering,$x2945-9168 ;$v12818 311 08$a3-030-89246-8 327 $aCoordination -- Protocol Scheduling -- Automated Replication of Tuple Spaces via Static Analysis -- Incremental Refinement of Goal Models with Contracts -- Logic -- Proof Calculi for Epistemic Logics with Structured Knowledge -- Introducing Intervalar differential dynamic logic -- A Program Logic for Fresh Name Generation -- Event-Driven Temporal Logic Pattern for Control Software Requirements Specification -- Extending OCL with map and function types -- Networks -- Deadlock in packet switching networks -- Runtime Monitoring Processes Across Blockchains -- Solving Systems of Bilinear Equations for Transition Rate Reconstruction -- Parallel Computation -- Term Rewriting on GPUs -- Promise Plus: Flexible Synchronization for Parallel Computations on Arrays -- Testing -- Towards Test Case Generation for Industrial Software Systems Based on Functional Specifications -- Compressing Automatically Generated Unit Test Suites through Test Parameterization -- Systematic Extractionof Test Cases from Object-oriented Programs. 330 $aThis book constitutes the thoroughly refereed post-conference proceedings of the 9th International Conference on Fundamentals of Software Engineering, FSEN 2021, held virtually and hosted by IPM in May 2021. The 12 full papers and 4 short papers presented in this volume were carefully reviewed and selected from 38 submissions. The topics of interest in FSEN span over all aspects of formal methods, especially those related to advancing the application of formal methods in the software industry and promoting their integration with practical engineering techniques. The papers are organized in topical sections on coordination, logic, networks, parallel computation, and testing. 410 0$aProgramming and Software Engineering,$x2945-9168 ;$v12818 606 $aSoftware engineering 606 $aMicroprogramming 606 $aComputer networks 606 $aComputer science 606 $aSoftware Engineering 606 $aControl Structures and Microprogramming 606 $aComputer Communication Networks 606 $aTheory of Computation 615 0$aSoftware engineering. 615 0$aMicroprogramming. 615 0$aComputer networks. 615 0$aComputer science. 615 14$aSoftware Engineering. 615 24$aControl Structures and Microprogramming. 615 24$aComputer Communication Networks. 615 24$aTheory of Computation. 676 $a005.1 700 $aHojjat$b Hossein$0905425 702 $aMassink$b Mieke 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910506376103321 996 $aFundamentals of software engineering$92897772 997 $aUNINA