(New Series) of The

VOLUME 29 NUMBER 2 OCTOBER 1993 ULLETIN (NEW SERIES) OF THE

EDITORS Haynes R. Miller, Research Announcements Richard S. Palais, Research-Expository Papers Murray H. Protter, Book Reviews

PROVIDENCE,RHOD: ISSN 0273-0979 Bulletin (New Series) of the American Mathematical Society This journal is devoted to articles of the following types: Research-Expository Papers These are, by definition, papers that present a clear and insightful exposition of significant aspects of contemporary mathematical research. Gibbs lectures, Progress in Mathematics lectures, and retiring presidential addresses will be included in this section. Research Announcements The purpose of this department is to publish quickly and disseminate widely significant new mathematics. A Research Announcement should be designed to communicate its contents to a broad mathematical audience and should meet high standards for clarity as well as mathematical content. Book Reviews Book Reviews are accepted for publication by invitation only. Unsolicited manuscripts will not be considered.

Subscription information. Bulletin (New Series) of the American Mathematical Society is published quarterly. Subscription prices for Volumes 28 and 29 (1993) are $217 list, $174 institutional member, $ 130 individual member. The subscription price for members is included in the annual dues. A late charge of 10% of the subscription price will be imposed upon orders received from non- members after January 1 of the subscription year. Subscribers outside the United States and India must pay a postage surcharge of $8.00; subscribers in India must pay a postage surcharge of $ 13.00. Expedited delivery to destinations in North America $12; elsewhere $21. Beginning in January 1992, the Bulletin will be available from the electronic service e-MATH [telnet e-MATH.ams.org (or telnet 130.44.1.100). Login and password are e-math] Back number information. For back issues see the AMS Catalog of Publications. Subscriptions and orders should be addressed to the American Mathematical Society, P. O. Box 5904, Boston, MA 02206-5904. All orders must be accompanied by payment. Other correspondence should be addressed to P. O. Box 6248, Providence, RI 02940-6248. Copying and reprinting. Individual readers of this publication, and nonprofit libraries acting for them, are permitted to make fair use of the material, such as to copy an article for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews, provided the customary acknowledgment of the source is given. Republication, systematic copying, or multiple reproduction of any material in this publication (including abstracts) is permitted only under license from the American Mathematical Society. Requests for such permission should be addressed to the Manager of Editorial Services, American Mathematical Society, P. O. Box 6248, Providence, RI 02940-6248. Requests can also be made by e-mail to reprint-permissionSmath. ams. org. The appearance of the code on the first page of an article in this journal indicates the copyright owner's consent for copying beyond that permitted by Sections 107 or 108 of the U.S. Copyright Law, provided that the fee of $1.00 plus $.25 per page for each copy be paid directly to the Copyright Clearance Center, Inc., 27 Congress Street, Salem, MA 01970. This consent does not extend to other kinds of copying, such as copying for general distribution, for advertising or promotional purposes, for creating new collective works, or for resale.

Bulletin (New Series) of the American Mathematical Society is published quarterly by the Amer- ican Mathematical Society at 201 Charles Street, Providence, RI 02904-2213. Second class postage is paid at Providence, Rhode Island, and additional mailing offices. Postmaster: Send address changes to Bulletin, American Mathematical Society, P. O. Box 6248, Providence, RI 02940-6248. © Copyright 1993 American Mathematical Society. All rights reserved. Printed in the United States of America. @ The paper used in this journal is acid-free and falls within the guidelines established to ensure permanence and durability. This publication was typeset using .Aa^S-TeX, the American Mathematical Society's TgX macro system. 10 9 8 7 6 5 4 3 2 1 98 97 96 95 94 93 Bulletin of the American Mathematical Society AUTHOR INDEX 1993, Volumes 28-29

RESEARCH-EXPOSITORYPAPERS

Bergweiler, Walter. Iteration of meromorphic functions, 29,151 Birman, Joan S. New points of view in knot theory, 28, 253 Chichilnisky, G. Intersecting families of sets and the topology of cones in economics, 29, 189 Howe, Roger E. and Tan, Eng-Chye. Homogeneous functions on light cones : The infinitesimal structure of some degenerate principal series representations, 28, 1 Hunt, Brian R., Sauer, Tim, and Yorke, James A. Prevalence: An addendum, 28, 306 "Theoretical Jaffe, Arthur and Quinn, Frank. Mathematics": Toward a cultural synthesis of mathematics and theoretical physics, 29, 1 Mazur, B. On the passage from local to global in number theory, 29, 14 Quinn, Frank. See Jaffe, Arthur Sauer, Tim. See Hunt, Brian R. Strang, Gilbert. Wavelet transforms versus Fourier transforms, 28, 288 Tadic, Marko. An external approach to unitary representations, 28, 215 Tan, Eng-Chye. See Howe, Roger E. Yorke, James A. See Hunt, Brian R. RESEARCHANNOUNCEMENTS Adem, Alejandro. Representations and K-theory of discrete groups, 28, 95 Barlow, Martin T. and Bass, Richard F. Coupling and Harnack inequalities for Sierpinski carpets, 29, 208 Bass, Richard F. See Barlow, Martin T. Becker, Howard and Kechris, Alexander S. Borel actions of Polish groups, 28, 334 Bryant, J., Ferry, S., Mio, W., and Weinberger, S. Topologyof homology manifolds, 28, 324 Bryson, Steve, Freedman, Michael H., He, Zheng-Xu, and Wang, Zhenghan. Móbius invariance of knot energy, 28, 99 Calderbank, A. R., Hammons, A. R., Jr., Kumar, P. Vijay, Sloane, N. J. A., and Solé, Patrick. A linear construction for certain Kerdock and Prepárala codes, 29, 218 Ferry, S. See Bryant, J. Freedman, Michael H. See Bryson, Steve Gesztesy, F., Holden, H., Simon, B., and Zhao, Z. Trace formulae and inverse spectral theory for Schrodinger operators, 29, 250 Gong, Guihua. Relative K-cycles and elliptic boundary conditions, 28, 104 Griggs, Jerrold R. On the distribution of sums of residues, 28, 329 Hammons, A. R., Jr. See Calderbank, A. R. Hannah, John and O'Meara, K. C. A new measure of growth for countable-dimensional algebras, 29, 223 Harrison, Jenny. Stokes'theorem for nonsmooth chains, 29,235 He, Zheng-Xu. See Bryson, Steve Heitmann, Raymond C. A counterexample to the rigidity conjecture for rings, 29, 94 Hoffman, David, Wei, Fusheng, and Karcher, Hermann. Adding handles to the helicoid, 29, 77 Holden, H. See Gesztesy, F. Hrushovski, Ehud and Zilber, Boris. Zariski geometries, 28, 315 Janssen, Jeannette C. M. The Dinitz problem solved for rectangles, 29, 243 Jiang, Tan and Yau, Stephen S.-T. Topological invariance of intersection lattices of arrangements in CP2, 29, 88 Jorgensen, Palle E. T. and Pedersen, Steen. Harmonic analysis of fractal measures induced by representations of a certain C-algebra, 29, 228 Kahn, Jeff and Kalai, Gil. A counterexample to Borsuk's conjecture, 29, 60 Kalai, Gil. See Kahn, Jeff Karcher, Hermann. See Hoffman, David Kechris, Alexander S. See Becker, Howard Kronheimer, P. B. The genus-minimizing property of algebraic curves, 29, 63 AUTHOR INDEX Kumar, P. Vijay. See Calderbank, A. R. Mio, W. See Bryant, J. O'Meara, K. C. See Hannah, John Pedersen, Steen. See Jorgensen, Palle E. T. Radin, Charles. Symmetry of tilings of the plane, 29,213 Ramm, A. G. and Zaslavsky, A. I. Singularities of the Radon transform, 28, 109 Riedel, Norbert. Absence of Cantor spectrum for a class of Schrödinger operators, 29, 85 Robertson, Neil, Seymour, P. D., and Thomas, Robin. Linkless embeddings of graphs in 7>-space, 28, 84 Rudolph, Lee. Quasipositivity as an obstruction to sliceness, 29, 51 Simon, B. See Gesztesy, F. Seymour, P. D. See Robertson, Neil Sloane, N. J. A. See Calderbank, A. R. Solé, Patrick. See Calderbank, A. R. Stahl, Herbert. Best uniform rational approximation of xa on [0,1], 28, 116 Thomas, Robin. See Robertson, Neil Wang, Zhenghan. See Bryson, Steve Wasilkowski, G. W. Integration and approximation of multivariate functions: average case complexity with isotropic Wiener measure, 28, 308 Weinberger, S. See Bryant, J. Wozniakowski, H. Average case complexity of linear multivariate problems, 29, 70 Wu, Lang-Fang. A new result for the porous medium equation derived from the Ricci flow, 28, 90 Wei, Fusheng. See Hoffman, David Zaslavsky, A. I. See Ramm, A. G. Zhang, Shuang. Factorizations of invertible operators and K-theory of C*-algebras, 28, 75 Zhao, Z. See Gesztesy, F. Zilber, Boris. See Hrushovski, Ehud BOOK REVIEWS Ball, J. A., Gohberg, I., and Rodman, L. Interpolation of rational matrix functions, reviewed by M. A. Kaashoek, 28, 426 Bainov, Drumi and Simeonov, Pavel. Integral inequalities and applications, reviewed by C. Corduneanu, 29, 282 Bartocci, Claudio, Bruzzo, Ugo, and Hernández-Ruipérez, Daniel. The geometry ofsupermanifolds, reviewed by Alice Rogers, 28, 184 Baues, Hans Joachim. Combinatorial homotopy and ^-dimensional complexes, reviewed by John R. Harper, 28, 408 Benson, D. J. Representations and cohomology, II: Cohomology of groups and modules, reviewed by J. E. Humphreys, 29, 262 Bertin, M. J., Decomps-Guilloux, A., Grandet-Hugot, M., Pathiaux-Delefosse, M., and Schreiber, J. P. Pisot and Salem numbers, reviewed by M. Mendes France, 29, 274 Böttcher, A. and Silbermann, B. Analysis of Toeplitz operators, reviewed by Thomas Kriete, 28, 387 Botvinnik, Boris I. Manifolds with singularities and the Adams-Novikov spectral sequence, reviewed by Douglas C. Ravenel, 29, 290 Brualdi, Richard A. and Ryser, Herbert J. Combinatorial matrix theory, reviewed by W. T. Tutte, 28, 202 Bruzzo, Ugo. See Bartocci, Claudio Chui, Charles K. An introduction to wavelets, reviewed by Yves Meyer, 28, 350 Conway, J. H. and Sloane, N. J. A. Sphere packings, lattices and groups, reviewed by C. A. Rogers, 29, 306 Conway, John. The theory of subnormal operators, reviewed by T. W. Gamelin, 28, 199 Cottle, R. W., Pang, J. S., and Stone, R. E. The linear complementarity problem, reviewed by M. C. Ferris, 28, 169 Daubechies, Ingrid. Ten lectures on wavelets, reviewed by Yves Meyer, 28, 350 Dautray, Robert and Lions, Jacques-Louis. Mathematical analysis and numerical methods for science and technology, Volume 5. Evolution problems 1, reviewed by Karen A. Ames, 29, 117 AUTHOR INDEX Decomps-Guilloux, A. See Bertin, M. J. Doerk, Klaus and Hawkes, Trevor. Finite soluble groups, reviewed by Cheryl E. Praeger, 29, 104 Donaldson, S. K. and Kronheimer, P. B. The geometry of four-manifolds, reviewed by N. J. Hitchin, 28,415 Dong, Guangchang. Nonlinear partial differential equations of second order, reviewed by Gary M. Lieberman, 28, 161 Dovermann, K. H. and Schultz, Reinhard. Equivariant surgery theories and their periodicity properties, reviewed by Mel Rothenberg, 28, 375 Dwork, Bernard. Generalized hypergeometric functions, reviewed by Alan Adolphson, 29, 279 Effinger, Gove W. and Hayes, David R. Additive number theory of polynomials over a finite field, reviewed by R. C. Vaughan, 28, 209 Eklof, Paul C. and Mekler, Alan H. Almost free modules. Set-theoretic methods, reviewed by Laszlo Fuchs, 28, 141 Engelbrecht, Juri. Introduction to asymmetric solitary waves, reviewed by John Albert, 28, 164 Evens, Leonard. The cohomology of groups, reviewed by Richard G. Swan, 29, 113 Falkovich, G. See Zakharov, V. E. Fujishige, S. Submodular functions and optimization theory, reviewed by Richard P. McLean and William W. Sharkey, 29, 98 Gohberg, I. See Ball, J. A. Golub, Gene H. and Ortega, James M. Scientific computing and differential equations—An introduction to numerical methods, reviewed by David M. Young, 28, 397 Grandet-Hugot, M. See Bertin, M. J. Gurarie, David. Symmetries and Laplacians : Introduction to harmonic analysis, group representations and applications, reviewed by Audrey Terras, 29, 144 Hawkes, Trevor. See Doerk, Klaus Hayes, David R. See Effinger, Gove W. Henstock, Ralph. The general theory of integration, reviewed by Robert G Bartle, 29, 136 Hernández-Ruipérez, Daniel. See Bartocci, Claudio Hinch, E. J. Perturbation methods, reviewed by James Murdock, 28, 418 Hodgson, C. D., Rivin, I., and Smith, W. D. Erratum, 28,213 Howe, Roger and Tan, Eng-Chye. Non-abelian harmonic analysis. Applications of SL(2, R), reviewed by David A. Vogan, Jr., 28, 176 Hin, A. M. Matching of asymptotic expansions of solutions of boundary value problems, reviewed by Julian D. Cole, 29, 270 Il'yashenko, Yu. S. Finiteness theorems for limit cycles, reviewed by Carmen Chicone, 28, 123 Jeffries, Clark. Code recognition and set selection with neural networks, reviewed by Morris W. Hirsch, 29, 256 Jensen, Kjeld Knudsen and Thomsen, Klaus. Elements of KK-theory, reviewed by Jonathan Rosenberg, 28, 342 Jost, Jürgen. Two-dimensional geometric variational problems, reviewed by Friedrich Sauvigny, 28, 206 Kaiser, Gerald. Quantum physics, relativity and complex spacetime, reviewed by Robert Hermann, 28, 130 Kharchenko, V. K. Automorphisms and derivations of associative rings, reviewed by P. M. Cohn, 28, 348 Klimek, Maciej. Pluripotential theory, reviewed by J. E. Fornaess, 28, 382 Ko, Ker-I. Complexity theory of real functions, reviewed by Marian Boykan Pour-El, 29, 271 Kostrikin, A. I. Around Burnside, reviewed by M. F. Newman and G. E. Wall, 28, 157 Kronheimer, P. B. See Donaldson, S. K. Kufner, A. See Opic, B. LeVeque, Randall J. Numerical methods for conservation laws, reviewed by John C. Strikwerda, 28, 370 Lions, Jacques-Louis. See Dautray, Robert Lvov, V. S. See Zakharov, V. E. Manin, Yuri I. Topics in non-commutative geometry, reviewed by Ivan Penkov, 29, 106 Marinov, C. A. and Neittaanmäki, P. Mathematical models in electrical circuits : theory and applications, reviewed by A. H. Zemanian, 28, 194 Medvedev, Fyodor A. Scenes from the history of real functions, reviewed by Angus E. Taylor, 28, 360 AUTHOR INDEX

Meirmanov, Anvarbek. The Stefan problem, reviewed by John Ockendon, 28, 421 Mekler, Alan H. See Eklof, Paul C. Meyer-Nieberg, Peter. Banach lattices, reviewed by C. D. Aliprantis, 28, 190 Mikhlin, Solomon G. Error analysis in numerical processes, reviewed by F. Stummel, 28, 204 Nash, Charles. Differential topology and quantum field theory, reviewed by Daniel S. Freed, 28, 153 Neittaanmäki, P. See Marinov, C. A. Neuman, Frantisek. Global properties of linear ordinary differential equations, reviewed by Anton Zettl, 29, 293 Odifreddi, P. Classical recursion theory, reviewed by J. R. Shoenfield, 28, 182 Opic, B. and Kufner, A. Hardy-type inequalities, reviewed by Hans P. Heinig, 28, 423 Ortega, James M. See Golub, Gene H. Pang, J. S. See Cottle, R. W. Pathiaux-Delefosse, M. See Bertin, M. J. Penner, R. C, with J. L. Harer. Combinatorics of train tracks, reviewed by W. Abikoff, 29, 130 Petkov, V. M. and Stoyanov, L. N. Geometry of reflecting rays and inverse problems, reviewed by J. Sjöstrand, 29, 124 Pohst, M. and Zassenhaus, H. Algorithmic algebraic number theory, reviewed by René Schoof, 29, 111 Popov, V. L. Groups, generators, syzygies, and orbits in invariant theory, reviewed by Gerald W. Schwarz, 29, 299 Ramm, Alexander G. Multidimensional inverse scattering problems, reviewed by Reese T. Prosser, 29, 139 Rivin, I. See Hodgson, C. D. Rodman, L. See Ball, J. A. Ryser, Herbert J. See Brualdi, Richard A. Sakai, Shôichirô. Operator algebras in dynamical systems, reviewed by Richard V. Kadison, 28, 133 Schreiber, J. P. See Bertin, M. J. Schultz, Reinhard. See Dovermann, K. H. Silbermann, B. See Böttcher, A. Simeonov, Pavel. See Bainov, Drumi Sloane, N. J. A. See Conway, J. H. Smith, W. D. See Hodgson, C. D. Stahl, Herbert and Totik, Vilmos. General orthogonal polynomials, reviewed by D. S. Lubinsky, 28, 403 Stone, R. E. See Cottle, R. W. Stoyanov, L. N. See Petkov, V. M. Struwe, Michael. Variational methods (Applications to nonlinear PDE and Hamiltonian systems), reviewed by Jürgen Jost, 28, 149 Ta-Tsien, Li and Yunmei, Chen. Global classical solutions for nonlinear evolution equations, reviewed by Walter A. Strauss, 29, 265 Tan, Eng-Chye. See Howe, Roger Tempelman, Arkady. Ergodic theorems for group actions, reviewed by H. O. Georgii, 29, 126 Thomsen, Klaus. See Jensen, Kjeld Knudsen Totik, Vilmos. See Stahl, Herbert Tromba, Anthony J. Teichmüller theory in Riemannian geometry, reviewed by Michael Wolf, 29, 285 Varadarajan, V. S. An introduction to harmonic analysis on semisimple Lie groups, reviewed by Joseph A. Wolf, 28, 367 Vaughan-Lee, Michael. The restricted Burnside problem, reviewed by M. F. Newman and G. E. Wall, 28, 157 Voss, Heinz-Jürgen. Cycles and bridges in graphs, reviewed by Cecil Rousseau, 28, 147 Vovsi, Samuel M. Topics in varieties of group representations, reviewed by Peter M. Neumann, 29, 120 Weder, Ricardo. Spectral and scattering theory for wave propagation in perturbed stratified media, reviewed by Calvin H. Wilcox, 28, 137 Weil, André. André Weil: The apprenticeship of a mathematician, reviewed by Saunders Mac Lane, 28, 144 AUTHOR INDEX Wesseling, P. An introduction to multigrid methods, reviewed by Steve McCormick, 28, 373 Wiggins, Stephen. Chaotic transport in dynamical systems, reviewed by Robert W. Easton, 28, 398 Yunmei, Chen. See Ta-Tsien, Li Zakharov, V. E., Lvov, V. S., and Falkovich, G. Kolmogorov spectra of turbulence I: Wave turbulence, reviewed by Alexandre J. Chorin, 29, 304 Zassenhaus, H. See Pohst, M. VOLUME29 1993

^NDED ULLETIN (NEW SERIES) OF THE

AMERICAN MATHEMATICAL SOCIETY

EDITORS Haynes R. Miller, Research Announcements Richard S. Palais, Research-Expository Papers Murray H. Protter, Book Reviews

ASSOCIATE EDITORS John Baez Zoltan Furedi Gregory L. Cherlin Jerry L. Kazdan David Donoho Harry Kesten William G. Dwyer Robert Lazarsfeld David Eisenbud Paul S. Muhly Charles L. Epstein Jeffrey Rauch Daniel S. Freed Kenneth Ribet Michael D. Fried

PROVIDENCE, RHODE ISLAND USA ISSN 0273-0979 Bulletin (New Series) of the American Mathematical Society This journal is devoted to articles of the following types: Research-Expository Papers These are, by definition, papers that present a clear and insightful exposition of significant aspects of contemporary mathematical research. Gibbs lectures, Progress in Mathematics lectures, and retiring presidential addresses will be included in this section. Research Announcements The purpose of this department is to publish quickly and disseminate widely significant new mathematics. A Research Announcement should be designed to communicate its contents to a broad mathematical audience and should meet high standards for clarity as well as mathematical content. Book Reviews Book Reviews are accepted for publication by invitation only. Unsolicited manuscripts will not be considered.

Subscription information. Bulletin (New Series) of the American Mathematical Society is published quarterly. Subscription prices for Volumes 28 and 29 (1993) are $217 list, $174 institutional member, $ 130 individual member. The subscription price for members is included in the annual dues. A late charge of 10% of the subscription price will be imposed upon orders received from non- members after January 1 of the subscription year. Subscribers outside the United States and India must pay a postage surcharge of $8.00; subscribers in India must pay a postage surcharge of $ 13.00. Expedited delivery to destinations in North America $12; elsewhere $21. Beginning in January 1992, the Bulletin will be available from the electronic service e-MATH [telnet e-MATH.ams.org (or telnet 130.44.1.100). Login and password are e-math.] Back number information. For back issues see the AMS Catalog of Publications. Subscriptions and orders should be addressed to the American Mathematical Society, P. O. Box 5904, Boston, MA 02206-5904. All orders must be accompanied by payment. Other correspondence should be addressed to P. O. Box 6248, Providence, RI 02940-6248. Copying and reprinting. Individual readers of this publication, and nonprofit libraries acting for them, are permitted to make fair use of the material, such as to copy an article for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews, provided the customary acknowledgment of the source is given. Republication, systematic copying, or multiple reproduction of any material in this publication (including abstracts) is permitted only under license from the American Mathematical Society. Requests for such permission should be addressed to the Manager of Editorial Services, American Mathematical Society, P. O. Box 6248, Providence, RI 02940-6248. Requests can also be made by e-mail to reprint-permissionSmath. ams . org. The appearance of the code on the first page of an article in this journal indicates the copyright owner's consent for copying beyond that permitted by Sections 107 or 108 of the U.S. Copyright Law, provided that the fee of $ 1.00 plus $.25 per page for each copy be paid directly to the Copyright Clearance Center, Inc., 27 Congress Street, Salem, MA 01970. This consent does not extend to other kinds of copying, such as copying for general distribution, for advertising or promotional purposes, for creating new collective works, or for resale.

Bulletin (New Series) of the American Mathematical Society is published quarterly by the Amer- ican Mathematical Society at 201 Charles Street, Providence, RI 02904-2213. Second class postage is paid at Providence, Rhode Island, and additional mailing offices. Postmaster: Send address changes to Bulletin, American Mathematical Society, P. O. Box 6248, Providence, RI 02940-6248. © Copyright 1993 American Mathematical Society. All rights reserved. Printed in the United States of America. @ The paper used in this journal is acid-free and falls within the guidelines established to ensure permanence and durability. This publication was typeset using .AyvfS-TjgX, the American Mathematical Society's TgX macro system. 109 8765432 1 98 97 96 95 94 93 BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY CONTENTS JULY 1993

Research-Expository Papers "Theoretical Mathematics": Toward a cultural synthesis of mathematics and theoretical physics by Arthur Jaffe and Frank Quinn. 1 On the passage from local to global in number theory by B. Mazur. 14 Research Announcements

Quasipositivity as an obstruction to sliceness by Lee Rudolph . 51 A counterexample to Borsuk's conjecture by Jeff Kahn and Gil Kalai. 60 The genus-minimizing property of algebraic curves by P. B. Kronheimer. 63 Average case complexity of linear multivariate problems by H. Wozniakowski ... 70 Adding handles to the helicoid by David Hoffman, Fusheng Wei, and Hermann Karcher. 77 Absence of Cantor spectrum for a class of Schrödinger operators by Norbert Riedel 85 Topological invariance of intersection lattices of arrangements in CP by Tan Jiang and Stephen S.-T. Yau. 88 A counterexample to the rigidity conjecture for rings by Raymond C. Heitmann . 94 Book Reviews Submodular functions and optimization theory by S. Fujishige—Reviewed by Richard P. McLean and William W. Sharkey . 98 Finite soluble groups by Klaus Doerk and Trevor Hawkes—Reviewed by Cheryl E. Praeger. 104 Topics in non-commutative geometry by Yuri I. Manin—Reviewed by Ivan Penkov 106 Algorithmic algebraic number theory by M. Pohst and H. Zassenhaus—Reviewed by René Schoof. Ill The cohomology of groups by Leonard Evens—Reviewed by Richard G. Swan_ 113 Mathematical analysis and numerical methods for science and technology, Volume 5. Evolution problems 1 by Robert Dautray and Jacques-Louis Lions—Reviewed by Karen A. Ames. 117 Topics in varieties of group representations by Samuel M. Vovsi—Reviewed by Peter M. Neumann. 120 Geometry of reflecting rays and inverse problems by V. M. Petkov and L. N. Stoyanov—Reviewed by /. Sjóstrand. 124 Ergodic theorems for group actions by Arkady Tempelman—Reviewed by H. O. Georgii. 126 Combinatorics of train tracks by R. C. Penner with J. L. Harer—Reviewed by W.Abikoff. 130 The general theory of integration by Ralph Henstock—Reviewed by Robert G. Bartle 136 Multidimensional inverse scattering problems by Alexander G. Ramm—Reviewed by Reese T. Prosser. 139 Symmetries and Laplacians: Introduction to harmonic analysis, group representations and applications by David Gurarie—Reviewed by Audrey Terras. 144 CONTENTS OCTOBER 1993

Research-Expository Papers Iteration of meromorphic functions by Walter Bergweiler. 151 Intersecting families of sets and the topology of cones in economics by G. Chichilnisky. 189 Research Announcements Coupling and Harnack inequalities for Sierpinski carpets by Martin T. Barlow and Richard F. Bass. 208 Symmetry of tilings of the plane by Charles Radin. 213 A linear construction for certain Kerdock and Preparata codes by A. R. Calderbank, A. R. Hammons, Jr., P. Vijay Kumar, N. J. A. Sloane, and Patrick Solé_ 218 A new measure of growth for countable-dimensional algebras by John Hannah and K. C. O'Meara. 223 Harmonic analysis of fractal measures induced by representations of a certain C- algebra by Palle E. T. Jorgensen and Steen Pedersen. 228 Stokes' theorem for nonsmooth chains by Jenny Harrison. 235 The Dinitz problem solved for rectangles by Jeannette C M. Janssen. 243 Trace formulae and inverse spectral theory for Schrödinger operators by F. Gesztesy, H. Holden, B. Simon, and Z. Zhao . 250 Book Reviews Code recognition and set selection with neural networks by Clark Jeffries—Reviewed by Morris W. Hirsch. 256 Representations and cohomology, II: Cohomology of groups and modules by D. J. Benson—Reviewed by /. E. Humphreys. 262 Global classical solutions for nonlinear evolution equations by Li Ta-Tsien and Chen Yunmei—Reviewed by Walter A. Strauss. 265 Matching of asymptotic expansions of solutions of boundary value problems by A. M. Hin—Reviewedby Julian D. Cole. 270 Complexity theory of real functions by Ker-I Ko—Reviewed by Marian Boykan Pour-El. 271 Pisot and Salem numbers by M. J. Bertin, A. Decomps-Guilloux, M. Grandet-Hugot, M. Pathiaux-Delefosse, and J. P. Schreiber—Reviewed by M. Mendes France 21A Generalized hypergeometric functions by Bernard Dwork—Reviewed by Alan Adolphson. 279 Integral inequalities and applications by Drumi Bainov and Pavel Simeonov— Reviewed by C Corduneanu. 282 Teichmüller theory in Riemannian geometry by Anthony J. Tromba—Reviewed by Michael Wolf. 285 Manifolds with singularities and the Adams-Novikov spectral sequence by Boris I. Botvinnik—Reviewed by Douglas C. Ravenel. 290 Global properties of linear ordinary differential equations by Frantisek Neuman— Reviewed by Anton Zettl. 293 Groups, generators, syzygies, and orbits in invariant theory by V. L. Popov— Reviewed by Gerald W. Schwarz. 299 Kolmogorov spectra of turbulence I: Wave turbulence by V. E. Zakharov, V. S. Lvov, and G. Falkovich—Reviewedby Alexandre J. Chorin. 304 Sphere packings, lattices and groups by J. H. Conway and N. J. A. Sloane—Reviewed by C A. Rogers. 306 Editorial Board for Research-Expository Papers John Baez Haynes R. Miller David Donoho Richard S. Palais, Chair David Eisenbud Kenneth Ribet Jerry Kazdan

Editorial Board for Research Announcements Gregory L. Cherlin Harry Kesten William G. Dwyer Robert Lazarsfeld Charles L. Epstein Haynes R. Miller, Chair Daniel S. Freed Paul S. Muhly Michael D. Fried Jeffrey Rauch Zoltan Furedi

Book Reviews Editor: Murray H. Protter Managing Editor: Murray H. Protter

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Information to Authors and Editors For Research-Expository Papers and Research Announcements, the first page must consist of a descriptive title, followed by an abstract that summarizes the article in language suitable for workers in the general field (algebra, analysis, etc.). The descriptive title should be short but informative; useless or vague "some "concerning" phrases such as remarks about" or should be avoided. The abstract should be a brief technical description of the new material. Then, for Research Announcements there should be an introductory section addressed to nonexperts describing the motivation, background, and significance of the results announced. Following the statement of results, there should be a sketch of proofs that may be addressed to experts. An announcement should not exceed 7 published pages, and preferably not exceed 5 pages. For Research-Expository Papers and Research Announcements, included with the footnotes to the paper, there should be the 1991 Mathematics Subject Classification representing the primary and secondary subjects of the article. This may be followed by a list of key words and phrases describing the subject matter of the article and taken from it. A list of the numbers may be found in the annual index of Mathemati- cal Reviews, published with the December issue starting in 1990, as well as from the electronic service e-MATH [telnet e-MATH.ams.org (or telnet 130.44.1.100). Login and password are e-math.] For journal abbreviations used in bibliogra- phies, see the list of serials in the latest Mathematical Reviews annual index. Authors are encouraged to supply electronic addresses when available. These will be printed after the postal address at the end of each article.

Electronically prepared manuscripts. The AMS encourages submission of electronically prepared manuscripts in Am^-YeX or Aj^S-^f&- because properly prepared electronic manuscripts save the author proofreading time and move more quickly through the production process. To this end, the Society "preprint" has prepared style files, specifically the amsppt style of Aj^aS-T^X. and the amsart style of Aa^S-MjtX, which will simplify the work of authors and of the production staff. Those authors who make use of these style files from the beginning of the writing process will further reduce their own effort. Electronically submitted manuscripts prepared in plain TgX or MgX do not mesh properly with the AMS production systems and cannot, therefore, real- ize the same kind of expedited processing. Users of plain TgX should have little difficulty learning A^aS-T^X.,and IAT^Xusers will find that A\^S-^TeX is the same as UTfiX with additional commands to simplify the typesetting of mathematics.

Guidelines for Preparing Electronic Manuscripts provides additional assis- tance and is available for use with either A/^S-T^X or AmS-I^T^X. Authors with FTP access may obtain Guidelines from the Society's Internet node e-MATH.ams.org (130.44.1.100). For those without FTP access Guidelines can be obtained free of charge from the e-mail address guide-elecQmath.ams.org (Internet) or from the Customer Services Department, American Mathematical Society, P.O. Box 6248, Providence, RI 02940-6248. When requesting Guide- lines, please specify which version you want.

At the time of submission, authors should indicate if the paper has been prepared using 4m

Electronic manuscripts should be sent to the Providence office immediately after the paper has been accepted for publication. Editors should require auth- hors to send their electronically prepared manuscripts to the Providence office in a timely fashion. They can be sent via e-mail to pub-submitQmath. ams. org (Internet) or on diskettes to the Publications Department, American Mathe- matical Society, P.O. Box 6248, Providence, RI 02940-6248. When submitting electronic manuscripts please be sure to include a message indicating in which publication the paper has been accepted. No corrections will be accepted electronically. Authors must mark their changes on their proof copies and return them to the Providence office. Copies of the paper should be sent directly to the appropriate Editor, and the author should keep one copy. For Research-Expository papers, two copies of the manuscript should be submitted to Professor Richard S. Palais, Depart- ment of Mathematics, Brandeis University, Waltham, MA 02154-9110. For Research Announcements, four copies of the manuscript should be submitted to Professor Haynes R. Miller, Room 2-237, Massachusetts Institute of Tech- nology, Cambridge, MA 02139-4307. Research Announcements can also be submitted electronically in the standard TgX formats to hrmQmath.mit.edu. Any inquiries concerning a paper that has been accepted for publication should be sent directly to the Editorial Department, American Mathematical Society, P. O. Box 6248, Providence, RI 02940-6248.

Remarks on Research Announcements The circulation of the Bulletin is larger by an order of magnitude than that of most research mathematics journals; it is received by essentially every member of the Society. Space is limited to around 40 Announcements each year. The following facts largely determine the qualities looked for in an An- nouncement: The results should be, roughly speaking, among the 40 most significant or interesting achievements in mathematics in the year. The paper should contain background material for nonexperts that indicates why the results are significant and interesting. Address the paper to as wide an audience as possible, not just to experts. Strive for clarity and precision. Avoid jargon and introduce the terminology necessary to understand the main results. If space considerations prevent a full development, delineate clearly what is not being explained and provide references. The proof sketch can be more technical. Ask a colleague to review your manuscript before you submit it. Even better, ask two colleagues, one whose work is close to yours, one whose work is farther away. (If you can't get two people you know to read your work before it is published, how many will want to read it after?) Ask for suggestions on how to improve the readability. An abstract and the 1991 Mathematics Subject Classification are required. Papers submitted without these will be delayed. (Continued front back cover)

Teichmüller theory in Riemannian geometry by Anthony J. Tromba—Reviewed by Michael Wolf. 285 Manifolds with singularities and the Adams-Novikov spectral sequence by Boris I. Botvinnik—Reviewedby Douglas C Ravenel. 290 Global properties of linear ordinary differential equations by Frantisek Neuman— Reviewedby Anton Zettl. 293 Groups, generators, syzygies, and orbits in invariant theory by V. L. Popov— Reviewedby Gerald W. Schwarz. 299 Kolmogorov spectra of turbulence I: Wave turbulence by V. E. Zakharov, V. S. Lvov, and G. Falkovich—Reviewedby Alexandre J. Chorin. 304 Sphere packings, lattices and groups by J. H. Conway and N.J. A. Sloane—Reviewed by C. A. Rogers. 306 BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY CONTENTS Volume 29, Number 2 October 1993

(Continued on inside back cover) nun11L 0273-0979(199310)29:2;l-#