LEADER 05408nam 2200685Ia 450 001 9910811308203321 005 20240404143836.0 010 $a1-282-75810-1 010 $a9786612758102 010 $a981-4273-65-1 035 $a(CKB)2490000000001580 035 $a(EBL)1679632 035 $a(OCoLC)696297982 035 $a(SSID)ssj0000440719 035 $a(PQKBManifestationID)11304039 035 $a(PQKBTitleCode)TC0000440719 035 $a(PQKBWorkID)10490708 035 $a(PQKB)10881948 035 $a(MiAaPQ)EBC1679632 035 $a(WSP)00000557 035 $a(Au-PeEL)EBL1679632 035 $a(CaPaEBR)ebr10422066 035 $a(CaONFJC)MIL275810 035 $a(EXLCZ)992490000000001580 100 $a20090806d2009 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aPerspectives in mathematical sciences$hII /$feditors, N.S. Narasimha Sastry ... [et al.] ; series editor: Sankar K. Pal 205 $a1st ed. 210 $aSingapore ;$aLondon $cWorld Scientific$dc2009 215 $a1 online resource (281 p.) 225 1 $aStatistical science and interdisciplinary research ;$vv. 8 300 $a"Platinum jubilee series". 311 $a981-4273-64-3 320 $aIncludes bibliographical references. 327 $aContents; Foreword; Preface; 1. Use of Resultants and Approximate Roots for Doing the Jacobian Problem S. S. Abhyankar; 1.1. Introduction; 1.2. Basic Technique; 1.3. Resultants and Discriminants; 1.4. Real Numbers and Approximate Roots; Epilogue; References; 2. Monodromy of Principal Bundles I. Biswas and A. J. Parameswaran; 2.1. Introduction; 2.2. Tannakian Category; 2.3. A Tannakian Category for a Pointed Curve; 2.4. Monodromy of a Strongly Semistable Principal Bundles; 2.5. More on Monodromy; 2.6. Bundles on Higher Dimensional Varieties; References 327 $a3. Oligomorphic Permutation Groups P. J. Cameron3.1. Introduction; 3.1.1. Permutation groups; 3.1.2. Oligomorphic permutation groups; 3.1.3. Topology; 3.1.4. Cycle index; 3.2. Connections; 3.2.1. Model theory; 3.2.2. Combinatorial enumeration; 3.3. Constructions; 3.3.1. Direct and wreath products; 3.3.2. Other examples; 3.4. Growth Rates; 3.5. Graded Algebras; 3.6. Group Structure; References; 4. Descriptive Set Theory and the Geometry of Banach Spaces G. Godefroy; 4.1. Introduction; 4.2. A Short Survey on Analytic Sets; 4.3. Bossard's Coding of Separable Banach Spaces; 4.4. Coanalytic Ranks 327 $a4.5. A New Direction: The Converse StatementsAcknowledgment; References; 5. Multiplicity-Free Homogeneous Operators in the Cowen- Douglas Class A. Kora?nyi and G. Misra; 5.1. Background Material; 5.2. Computation of the Multipliers for the Unit Disc; 5.3. Conditions Imposed by the Reproducing Kernel; 5.4. The Multiplicity-Free Case; 5.5. Examples; References; 6. The Standard Conjectures on Algebraic Cycles M. S. Narasimhan; 6.1. The Case of Complex Projective Varieties; 6.2. Standard Conjectures in Abstract Algebraic Geometry; References 327 $a7. On the Classification of Binary Shifts on the Hyperfinite II 1 Factor G. L. Price7.1. Introduction; 7.2. Preliminaries; 7.3. Bitstreams and Polynomials; 7.4. Counting Polynomials with Symmetry; 7.5. Conjugacy Classes of Binary Shifts; References; 8. Symmetric and Quasi-Symmetric Designs and Strongly Regular Graphs S. S. Sane; 8.1. Introduction and Preliminaries; 8.2. Symmetric Designs; 8.3. Strongly Regular Graphs; 8.4. Quasi-Symmetric Designs; Acknowledgments; References; 9. Perturbation Determinant, Krein's Shift Function and Index Theorem K. B. Sinha; 9.1. Introduction 327 $a9.2. Perturbation Determinant9.3. Witten Index and Its Invariance; 9.4. Krein's Shift Function; 9.5. Application to Quantum Mechanics and Generalized Levinson's Theorem; References; 10. Zero Cycles and Complete Intersection Points on A.ne Varieties V. Srinivas; References; 11. Root Numbers and Rational Points on Elliptic Curves R. Sujatha; 11.1. Elliptic Curves and the Birch and Swinnerton-Dyer Conjecture; 11.2. Congruent Number Problem; 11.3. Root Numbers and the Parity Conjecture; 11.4. Recent Results; 11.5. Examples and Applications; References 327 $a12. von Neumann Algebras and Ergodic Theory V. S. Sunder 330 $a This book presents a collection of invited articles by distinguished Mathematicians on the occasion of the Platinum Jubilee Celebrations of the Indian Statistical Institute, during the year 2007. These articles provide a current perspective of different areas of research, emphasizing the major challenging issues. Given the very significant record of the Institute in research in the areas of Statistics, Probability and Mathematics, distinguished authors have very admirably responded to the invitation. Some of the articles are written keeping students and potential new entrants to an area of ma 410 0$aStatistical science and interdisciplinary research ;$vv. 8. 606 $aProbabilities 606 $aStatistics 615 0$aProbabilities. 615 0$aStatistics. 676 $a510 676 $a519.2 701 $aNarasimha Sastry$b N. S$01687295 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910811308203321 996 $aPerspectives in mathematical sciences$94060669 997 $aUNINA