Izrail M. Gelfand : Collected Papers III

Gelfand I.M. Collected papers In three volumes. vol.3 (Springer,1989)(ISBN 3540193995)(600dpi)(1087p) ......Page 3
Сopyright II ......Page 4
Preface III......Page 5
Foreword V......Page 6
Table of contents VII ......Page 8
Part I. Integral geometry 1 ......Page 12
1. Integral transformations connected with straight line complexes in a complex affine space (with M.I. Graev) 3 ......Page 14
2. Integral geometry on A>dimensional planes (with M.I. Graev and Z.Ya. Shapiro) 7......Page 18
3. Complexes of A:-dimensional planes in the space C\" and Plancherel’s formula for the group GL(n,C) (with M.I. Graev) 21......Page 32
4. Complexes of straight lines in the space C1 (with M.I. Graev) 26 ......Page 37
5. Differential forms and integral geometry (with M.I. Graev and Z.Ya. Shapiro) 37 ......Page 48
6. Integral geometry in projective space (with M.I. Graev and Z.Ya. Shapiro) 51 ......Page 62
7. A problem of integral geometry connected with a pair of Grassmann manifolds (with M.I. Graev and Z.Ya. Shapiro) 68 ......Page 79
8. Nonlocal inversion formulas in real integral geometry (with S.G. Gindikin) 73 ......Page 84
9. A local problem of integral geometry in a space of curves (with S.G. Gindikin and Z.Ya. Shapiro) 80 ......Page 91
10. A problem of integral geometry in RPn connected with the integration of differential forms (with S.G. Gindikin and M.I. Graev) 96 ......Page 107
11. Integral geometry in affine and projective spaces (with S.G. Gindikin and M.I. Graev) 99 ......Page 110
12. Geometric structures of double bundles and their relation to certain problems in integral geometry (with G.S. Shmelev) 228 ......Page 239
13. The problem of integral geometry and intertwining operators for a pair of real Grassmannian manifolds (with M. I. Graev and R. Rosu) 241 ......Page 252
14. On a characterization of Grassmann manifolds (with A.B. Goncharov) 266 ......Page 277
Part II. Cohomology and characteristic classes 271......Page 282
1. On classifying spaces for principal fiberings with Hausdorff bases (with D.B. Fuks) 273 ......Page 284
2. Topology of noncompact Lie groups (with D.B. Fuks) 277 ......Page 288
3. The cohomologies of the Lie algebra of the vector fields in a circle (with D.B. Fuks) 288 ......Page 299
4. Cohomologies of the Lie algebra of tangential vector fields of a smooth manifold (with D.B. Fuks) 290 ......Page 301
5. Cohomology of the Lie algebra of formal vector fields (with D.B. Fuks) 307......Page 318
6. Cohomologies of Lie algebra of tangential vector fields II (with D.B. Fuks) 323 ......Page 334
7. Cohomologies of Lie algebra of vector fields with nontrivial coefficients (with D.B. Fuks) 330 ......Page 341
8. Quadratic forms over commutative group rings and the K-theory (with A. S. Mishchenko) 342 ......Page 353
9. Upper bounds for cohomology of infinite-dimensional Lie algebras (with D.B. Fuks) 347 ......Page 358
10.The actions of infinite-dimensional Lie algebras (with D.B. Fuks and D.A. Kazhdan) 349 ......Page 360
11.Cohomology of the Lie algebra of Hamiltonian formal vector fields (with D.B. Fuks and D.I. Kalinin) 354 ......Page 365
12.PL Foliations (with D.B. Fuks) 358 ......Page 369
13. Cohomologies of the Lie algebra of formal vector fields with coefficients in its adjoint space and variations of characteristic classes of foliations (with B.L. Feigin and D.B. Fuks) 365 ......Page 376
14. The Gauss-Bonnet theorem and the Atiyah-Patodi-Singer functionals for the characteristic classes of foliations (with D.B. Fuks and A.M. Gabrielov) 379 ......Page 390
15.PL Foliations II (with D.B. Fuks) 403 ......Page 414
16. Combinatorial computation of characteristic classes (with A.M. Gabrielov and M.V. Losik) 407 ......Page 418
17. Combinatorial computation of characteristic classes (with A. M. Gabrielov and M. V. Losik) 420 ......Page 431
18. A local combinatorial formula for the first class of Pontryagin (with A.M. Gabrielov and M.V. Losik) 437 ......Page 448
19. Atiyah-Patodi-Singer functionals for characteristic functionals for tangent bundles (with A.M. Gabrielov and M.V. Losik) 441 ......Page 452
20. Computing of characteristic classes of combinatorial vector bundles (with M.V. Losik) 454 ......Page 465
21. Cohomology of infinite-dimensional Lie algebras and Laplace operators (with B.L. Feigin and D.B. Fuks) 487 ......Page 498
22. Geometry in Grassmannians and a generalization of the dilogarithm (with R.D. MacPherson) 492 ......Page 503
Part III. Functional integration; probability; information theory 527 ......Page 538
1. Generalized random processes 529 ......Page 540
2. Integration in functional spaces and its applications in quantum physics (with A.M. Yaglom) 534 ......Page 545
3. To the general definition of the amount of information (with A.N. Kolmogorov and A.M. Yaglom) 556 ......Page 567
4. Calculation of the amount of information about a random function contained in another such function (with A.M. Yaglom) 560 ......Page 571
Part IV. Mathematics of computation; cybernetics; biology 609 ......Page 620
1. On the application of the method of random tests (the Monte Carlo method) for the solution of the kinetic equation (with N.N. Chentsov,S.M. Fejnberg, and A. S. Frolov) 611 ......Page 622
2. On difference schemes for the solution of the equation of thermal conductivity. The double sweep method for solution of differenceequations (with O.V. Lokytsievskij) 617 ......Page 628
3. Some methods of control for complex systems (with M. L. Tsetlin) 648 ......Page 659
4. Determination of crystal structure by the method of nonlocal search (with Yu.G. Fedorov and 1.1. Piatetski-Shapiro) 671 ......Page 682
5. Determination of crystal structures by the method of the R-factor minimization (with Yu.G. Fedorov, R. A. Kayushina, and B.K. Vainstein) 675 ......Page 686
6. On certain classes of games and automata games (with 1.1. Piatetski-Shapiro and M.L. Tsetlin) 680 ......Page 691
7. Some problems in the analysis of movements (with V.S. Gurfinkel,M.L. Shik, and M.L. Tsetlin) 686 ......Page 697
8. Recordings of neurones of the dorsal spinocerebellar tract during evoked locomotion (with Yu. I. Arshavskij, M.B. Berkenblit, O.I. Fukson, and G.N. Orlovskij) 703 ......Page 714
9. Origin of modulation in neurones of the ventral spinocerebellar tract during locomotion (with Yu.I. Arshavskij, M.B. Berkenblit, O.I. Fukson, and G.N. Orlovskij) 707 ......Page 718
10. Generation of scratching I. Activity of spinal interneurons during scratching (with M.B. Berkinblit, T.G. Delyagina, A.G. Fel’dman,and G.N. Orlovskij) 711......Page 722
11. The cerebellum and control of rhythmical movements (with Yu.I. Arshavskij and G.N. Orlovskij) 729 ......Page 740
12. Interrelationships of contacting cells in the cell complexes of mouse ascites hepatoma (with V. I. Guelstein, A. G. Malenkov, and Yu.M. Vasil’ev) 735 ......Page 746
13. Initiation of DNA synthesis in cell cultures by colcemid (with V.I. Guelstein and Yu.M. Vasil’ev)747 ......Page 758
14. Mechanisms of morphogenesis in cell cultures (with Yu. M. Vasil’ev) 750 ......Page 761
15. Possible common mechanism of morphological and growth-related alterations accompanying neoplastic transformation (with Yu.M. Vasil’ev) 866 ......Page 877
16. Special type of morphological reorganization induced by phorbol ester: Reversible partition of cell into mobile and stable domains (with V.B. Dugina, T.M. Svitkina, and Yu.M. Vasil’ev) 870 ......Page 881
Part V. General theory of hypergeometric functions 875 ......Page 886
1. General theory of hypergeometric functions 877 ......Page 888
2. Generalized hypergeometric equations (with S. I. Gelfand) 882 ......Page 893
3. A duality theorem for general hypergeometric functions(with M.I. Graev) 886 ......Page 897
4. Algebraic and combinatorial aspects of the general theory of hypergeometric functions (with A. V. Zelevinskij) 891......Page 902
5. Combinatorial geometries, convex polyhedra, and Schubert cells(with M.Goresky, R.D. MacPherson, and V. V.Serganova) 906 ......Page 917
6. Strata of a maximal torus in a compact homogeneous space (with V. V. Serganova) 922 ......Page 933
7. Combinatorial geometries and torus strata on homogeneous compact manifolds (with V. V. Serganova) 926 ......Page 937
8. General hypergeometric functions on complex Grassmannians (with V. A. Vasiliev and A. V. Zelevinskij) 959 ......Page 970
9. Holonomie systems of equations and series of hypergeometric type (with M.I. Graev and A.V. Zelevinskij) 977 ......Page 988
10. On Heaviside functions of configuration of hyperplanes (with A.N. Varchenko) 983 ......Page 994
11. Arrangement of real hyperplanes and the associated partition function (with T.V. Alekseevskaya and A.V. Zelevinskij) 1006 ......Page 1017
12. Generalized Airey functions, Schubert cells and Jordan groups (with V.S. Retakh, V.V. Serganova) 1011......Page 1022
Appendix 1017 ......Page 1028
Cardiac arrhythmias and circle mappings (by V. I. Arnold) 1019 ......Page 1030
An Editorial Perspective (by B. Kostant) 1025 ......Page 1036
Table of contents for volumes I and II 1027 ......Page 1038
Bibliography 1033 ......Page 1044
Acknowledgements 1075 ......Page 1086
cover ......Page 1