Music by Design: A Sesquicentennial Statistics Songbook

Abstract

Fox, J. (1997), Applied Regression Analysis, Linear Models, and Related Methods, Thousand Oaks, CA: Sage Publications.

French, S., and Smith, J. Q. (eds.) (1997), The Practice of Bayesian Analysis, New York: Wiley.

Hettmansperger, T. P., and McKean, J. W. (1998), Robust Nonparametric Statistical Methods, London: Arnold.

Jacoby, W. G. (1998), Statistical Graphics For Visualizing Multivariate Data, Thousand Oaks, CA: Sage Publications.

Johnson, N. L., and Balakrishnan, N. (1997), Advances in the Theory and Practice of Statistics: A Volume in Honor of Samuel Kotz, New York: Wiley.

Korner, T. W. (1995), The Pleasures of Counting, Cambridge, U.K.: Cambridge University Press.

McLachlan, G. J., and Krishman, T. (1996), The EM Algorithm and Extensions, New York: Wiley.

Ruelle, D. (1991), Chance and Chaos, Princeton, NJ: Princeton University Press.

Ryan, T. P. (1997), Modern Regression Methods, New York: Wiley.

Bernstein, D. (1997), Statistical Applications of Baseball, Alexandria, VA: SPSTATE.     

Book reviews

Griffiths, D.F. (ed.):Numerical Analysis. Proceedings of the 10th Biennial Conference held at Dundee, Scotland, Jun 28-Juli 1, 1983. Lecture Notes in Mathematics. Vol. 1066. SpringerVerlag Berlin, Heidelberg, New York, Tokyo 1984, XI, 275 p. DM 33.50, ISBN 2-540-13344-5.

Gross, D.; C.M. Harris:Fundamentals of Queueing Theory. 2. Ed. John Wiley & Sons Limited New York, Chichester, Brisbane, Toronto 1985, XII, 587 p., £ 43.95, ISBN0-471-89067-7.

Miklosöko.; J.E.Kotov (eds.):Algorithms, Software and Hardware of Parallel Computers. Springer-Verlag Berlin, Heidelberg, New York, Tokyo 1984, 181 figs., 380 p., DM 89,-,ISBN 3-540-13657-6.

Dolcetta, I.C.; W.H. Fleming; T.Zolezzr (eds.):Recent Mathematical Methods in Dynamic Programming. Proceedings Corti. Rome, Mar 26-28, 1984. Lecture Notes in Mathematics. Vol. 1119. Springer-Verlag Berlin, Heidelberg, New York, Tokyo 1985, VI, 202 S.DM 31,50, ISBN 3-540-15217-2.

Demyanov, V.F.; D.Pallaschke (eds.):Nondifferentiable Optimization:Motivations and Applications. Proceedings, Sopron, Hungary 1984. Lecture Notes in Economics and Mathematical Systems. Vol. 255. Springer-Verlag Berlin, Heidelberg, New York, Tokyo 1985, VI, 349 S.

Kiwiel, K.C.:Methods of Descent for Nondifferentiable Optimization. Lecture Notes in Mathematics. VoL 1133. Springer-Verlag Berlin, Heidelberg, New York, Tokyo 1985, 'T1, 362 S., DM 51,50, ISBN 3-540-15642-9.

Remmert, R.:Funktionentheorie. Vol. 1. Grundwisaen Mat.hematik. Vol. 5. Springer-Verlag Berlin, Heidelberg, New York, Tokyo 1984, 65 Abb., XIII, 324 S., DM 44,-, ISBN:3;540-12782-8.

Walsh, G. R.:An Introduction to Linear Programming. 2. Ed. John Wiley & Sons Chichester, New York, Brisbane, Toronto, Singapore 1985, IX, 240 p., ISBN 0-471-90719-7.

Törnig, W.;M. Kaspar:Numerische Ldsung von partiellen Differentialgleichungen der Technik. Mathematische Methoden in der Technik.. Bd.. 1. B. G. Teubner Stuttgart 1985, 181 S., DM 34,-, ISBN 3-519-02613-9.

Neunzert, H.(ed.):Proceedings of the Conference JIathematics in Industry, Oct 24 - 28, 1983 Oberwolfach. B. G. Teubner Stuttgart 1984, 287 S., 52,- DM, ISBN 3-519-02610-4.

Lösch, M.:Fixpunkt-Schätzvertahren für Modelle mit rationaien Erwartungen.. Mathematical Systems in Economics:" Vol. 94. Verlagsgruppe Athenäum, Hain, Hanstein Königstein 1984; 312 S.,DM 68,-,ISBN 3-445-02387-5.

Bultheel, A.; P.Dewilde (eds.):Rational Approximation in Systems Engineering. Birkhäuser Verlag Basel 1983, 244 pp., sFr. 72,-. ISBN 3-7643-3159-3.

Harrison, J. M.:Brownian ])Iotion and Stochastic Flow Systems. John Wiley & Sons New York, Chichester, Brisbane 1985, XIX, 140 pp., 36.95 £ ISBN 471-81939-5.     

Book reviews

Desch, W.; F. Kappel; K. Kunisch: Estimation and Control of Distributed Parameter Systems. International Series of Numerical Mathematics. Vol. 100. Birkhauser Verlag AG Base1 1991, 396pp., DM 138, ISBN 3-7643-2676-X.

Klein, D. J.; M. RandiC: Mathematical Chemistry. Proceedings of the 3rd International Conference on Mathematical Chemistry, Galveston (USA) March 1989. VCH Weinheim 1990, 416pp., 59 fig., DM265,ISBN 3-527-28240-0.

Mezey, P. C.: Mathematical Modeling in Chemistry. VCH Weinheim 1991,416 pp., DM 265,ISBN 3-527-28292-0.

Lewandowski, A.; V. Volkovich (eds.): Multiobjective Problems of Mathematical Programming. Proceedings Yalta, USSR 1988. Lecture Notes in Economics and Mathematical Systems, Vol. 351. Springer-Verlag Berlin, Heidelberg, New York, London 1991, VII, 314 pp., Softcover, DM 61,- ISBN 3-540-532-6

Guddat, J.; F. Guerra Vasquez; H. Th. Jongen: Parametric Optimization: Singularities, Pathfollowing and Jumps. John Wiley & Sons Ltd. Baffins Lane, Chichester 1990, 216 pp., $80.40, ISBN 0-471-92807-0.

van der Geer, G.; F. Oort; J. Steenbrink (eds.): Arithmetic Algebraic Geometry. Progress in Mathematics, Vol. 89. Birkhauser Verlag Basel, Boston, Berlin l991, 446 pp., SFr. 78.-, ISBN 3-7643-3513-0.

Solomon, A.: PC Viruses-Detection, Analysis and Cure. Springer Verlag Berlin, Heidelberg, New York, Paris, London 1991, IX, 288 pp., DM 74,ISBN 3-540-19691-9.     

Book review

M. C. Kemp, Kimura: Introduction ot Mathematical Economics. Springer - Verlag New York - Heidelberg - Berlin, 1978, 249 S., DM 42.     

Book reveiw

VAK GELDROP, J. H.:A Mathematical Theory of Pure Exchange Economics without the No-Critical-Point Hypothesis. Mathernatical Centre tracts, 140. Mat.hemabisch Ce ntrum Amsterdam 1981, 108 S., 10 Abb., Dfl. 13.65.

J. K. SENGUPTA: Optimal Decisions under Uncertainty. Lecture Notes in Economics and Mathematical Systems, Vol. 193, Brosch., Springer-Verlag, Berlin, Heidelberg, New York, 1981, 156 S., DM 28.

LANGROCK, P.;W. JAHN:Einführung in die 'I'heorie der MARKOWSchen Ketten und ihre Anwendungen, Mathematisch-Naturwissenschaftliche Bibliothek Bd. 49. B. G. Teubner Verlagsgesellschaft Leipzig 1979, 268 S., 29,-M.

REETZ, D.A.:Kontrahierende endliehe MARKovscbe Entseheldungsprozesse. M + M Wissenschaftsverlag Berlin 1980, 262 S.

ROLSKI, T.: Stationary Random Processes Associated with Point Processes. Lecture Notes in Statistics, VoL 5. Berlin, New York 1981, VI + 139 S., DM 25.

GILL, P.E.;W. MURRAY, M.M. WRIGHT:Practical Optimization. Academic Press New York, London 1981, XVI + 402 S., ;£ 19.20.     

Book reviews

L.C.W.Dixon, G.P.Szegö{eds.}: Towards Global Optimisation.. North-Holland Publishing Company, Amsterdam 1975, 472 S., Dfl 95,00.

L.R.A.Casse, W.D.Wallis (eds.): Combinatorial Mathematics IV.. Proceedings of the Fourth Australian Conference, Held at the University of Adelaide, August 27-29, i975. Lecture Notes in Mathematics 560, Springer Verlag, Berlin-Hoidelberg-New York 1976" VII +249 S., DM 24,80.

R.Glowinski, J.L.Lions (eds.): Computing Methods in Applied Sciences and Engineering. Second International Symposium, December 15-19, 1975. Lecture Notes in Economics and Mathematical Systems, Vol. 134. Springer-Verlag Berlin-Heidelberg-New York 1976, VIII +390 S., DM 37.

E.Bohl,L.Collatz, K.P.Hadeler (Hrsg.): Numerik und Anwendungen von Eigenwertaufgaben und Verzweigungsproblemen. Vortragsauszüge der Tagung über Numerik und Anwendung von Eigenwerteufgaben und Verzweigungsproblemen vom 14.-20. November 1976 im Mathematischen Forschungsinstitut Oberwolfach (Schwarzwald). Internationale Schriftenreihe zur Numerischen Mathematik, Vol. 38. Birkhäuser-Verlag Basel 1977, 218 S., sir 42.     

Book review

Pereyra, V.;A.Reinoza (eds.): Numerical Methods. Proceedings of the international Work-shpop, Caracas, 1982 Lecture Notes in Mathematics Vol. 1005. Springer Verlag Berlin, Heidelberg, New York, Tokyo 1983, V, 296 P., DM 39, ISBN 3.540-12334-2.     

Book Reviews

Linear Algebra, 2nd edition by Serge Lang (1971). Addison-Wesley Publishing Company.

Linear Algebra with Applications by Hugh G. Campbell. Appleton-Century-Crofts, New York, 1971. xiii + 396 pp. + A45.An Engineering Approach to Linear Algebra, by W. W. Sawyer. Cambridge University Press, Cambridge, 1972. 304 pp. ($11.50)

An Engineering Approach to Linear Algebra, By W. W. Sawyer. Cambridge University Press, Cambridge, 1972. 304 pp. ($11.50) Sparse Matrices, by R. P. Tewarson. ($11.95)

Sparse Matrices, by R. P. Tewarson. ($11.95)     

Book Reviews

Linear Algebra, 2nd edition by Serge Lang (1971). Addison-Wesley Publishing Company.

Linear Algebra with Applications by Hugh G. Campbell. Appleton-Century-Crofts, New York, 1971. xiii + 396 pp. + A45.An Engineering Approach to Linear Algebra, by W. W. Sawyer. Cambridge University Press, Cambridge, 1972. 304 pp. ($11.50)

An Engineering Approach to Linear Algebra, By W. W. Sawyer. Cambridge University Press, Cambridge, 1972. 304 pp. ($11.50) Sparse Matrices, by R. P. Tewarson. ($11.95)

Sparse Matrices, by R. P. Tewarson. ($11.95)     

Book reviews

Devroye, L.; L. Györfi: Nonparametric Density Estimation: the L1 View. John Wiley & Sons New York, Chichester, Brisbane, Toronto, Singapore 1985, XI, 356 p., £ 45.90, ISBN 0-471816469

Gericke, H.: Mathematik in Antike und Orient. Springer-Verlag Berlin, Heidelberg, New York, Tokyo 1984, 140.Abb., 4 Kartenskizzen, XII, 292 S., DNI 98,-, ISBN 3-540-11647-8

K. ITö (ed.) StochasticAnalysis. Proceedings of the Traniguchi Internationaloal Symposium on Stochastic Analysis, Katata and Kyoto, 1982. North-Holland Mathematical Library, Vol. 32, North-Holland Publishing Company, Amsterdam 1984, 488 pages, Dfl. 250.- ISBN 0-444-87588-3

Weizenbaum, J.: Die Macht der Computer und dic Ohnmaeht der Vernuutt, Suhrkamp Taschenbuch Wissenschaf't 274. Suhrkamp Verlag Frankfurt/M. 1978, 368 S., DM 16,-, ISBN 3-518-27874-6

Krylov, N.V.; R. Sh. Lipiser; A.A Novikov (eds.): Statistics and Control of Stochastic Processes. Steklov Seminar, 1984. Springer-Verlag Berlin, Heidelberg, New York, Tokyo 1985, XIII, 507 S., DM 198, -, ISBN 3.540-96101-1

Sachs, H. (ed.): Graphs, Hypergraphs and Applications. Proceedings of the Conference on Graph Theory held in Eyba, Oct. 1984.. 'I'eubner-Texte zur Mathematik 73 Teubner Verlagsgesellschaft Leipzig 1985, 224 S., 23,-M, ISBN 666275-5

Bhat, U. Narayan; Elements of Applied Stochastic Processes. 2. Ed. Jonoh Wilet & Sons New York, Chichester, Brisbane, Toronto, Singapore 1984, IX, 685 p., £ 52.00, ISBN 0-471-87826-X

Methods of Operations Research. Bd, 66. Verlag Anton Hain Meisenheim, Königstein 1985, 410 S., DM 120,-, ISBN 3..445..02400..6

Maier, T.: Intervall-Input-Ontput-Rechnung. Mathernat.ical Systems in Economics. 101. Verlag Anton Rain, Meisenheim GmbH InigiteinTs. 1985, X, 338 S., DM 72,-, ISBN 3-445-02399-9.

Sawaragi, Y.; H. Nakayama; T. Tanino: Theory of Multi-objective Optimization. Mathematics in Science and Engineering. 176. Academic Press Orlando, San Diego, New York, London, Toronto 1985, 320 pp., $ 48.00, ISBN 0-12-620370-9.

Krämer, W.: Trend in ökonometrischen Modellen. Mathematical Systems in Economics. 93. Athenaum/Hain Konigstein 1985, 172 S., DM 48,-, ISBN 3-445-02386-7.     

Book reviews

d'Alessandro, P., A Conical Approach to Linear Programming Scalar and Vector Optimization Problems, Gordon and Breach Science Publishers, Australia Canada China France Germany India Japan Luxembourg Malaysia The Netherlands Russia Singapore Switzerland Thailand United Kingdom 1997, 312 pp., ISBN 90- 5699-031-4.

Fang, S.-C., Rajasekera, J. R. and Tsao, H. S. J., Entropy Optimization and Mathematical Programming, Kluwer's International Series. Kluwer Academic Publishers, Boston London Dordrecht, 1997, pp. 343, US $120.00; ISBN 0-7923-9939-0.

Golshtein, E. G. and Tretyakov, N. V., Modified Lagrangians Monotone Maps in Optimization, John Wiley & Sons, New York Chicester Brisbane Toronto Singapore 1996,438 pp., £55.00, ISBN 0-471-54821-9.

Hoffmann, K.-H., Leugering, G. and Troltzsch, F. (Eds.), Optimal Control of Partial Differential Equations, International Confa-ence in Chemnitz, Germany, April 20-25, 1998; International Series of Numerical Mathematics ISNM, Vol. 133, Birkhauser Verlag AG, Basel*Boston-Berlin 1999, viii+323 pp., DM 188.00, ISBN 3-7643- 6151-4.     

A Simplified Elementary Proof of Hadwiger's Volume Theorem

One of the most important results in geometric convexity is Hadwiger's characterization of quermassintergrals and intrinsic volumes. The importance lies in that Hadwiger's theorem provides straightforward proofs of numerous results in integral geometry such as the kinematic formulas [Santaló, L. A.: Integral Geometry and Geometric Probability, Addison-Wesley, 1976], the mean projection formulas for convex bodies [Schneider, R.: Convex Bodies: The Brunn—Minkowski Theory, Cambridge Univ. Press, 1993], and the characterization of totally invariant set functions of polynomial type [Chen, B. and Rota, G.-C.: Totally invariant set functions of polynomial type, Comm. Pure Appl. Math. 47 (1994), 187–197]. For a long time the only known proof of Hadwiger's theorem was his original one [Hadwiger, H.: Vorlesungen über Inhalt, Oberfläche and Isoperimetrie, Springer, Berlin, 1957] (long and not available in English), until a new proof was obtained by Klain [Klain, D. A.: A short proof of Hadwiger's characterization theorem, Mathematika 42 (1995), 329–339., Klain, D. A. and Rota, G.-C.: Introduction to Geometric Probability, Lezioni Lincee, Cambridge Univ. Press, 1997], using a result from spherical harmonics. The present paper provides a simplified and self-contained proof of Hadwiger's theorem.     

Book reviews

INtroduction to Group Characters, by Lederman, L.A.M.A., Cambridge University Press, 1977.

Matrix Representations in the Theory of Finite Groups, by V. A. Belonogov and A. N. Fomin. Nauka, Moscow, 1976 (in Russian). 48 kopecks.

Transformation Groups, Czes Kosniowski, Editor. London Mathematical Society Lecture Notes 26. Cambridge University Press, New York, 1977.     

Letters to the Editors

Abstract

Markov Chain Monte Carlo in Practice by W. R. Gilks, S. Richardson, and D. J. Spiegelhalter, New York: Chapman &; Hall, 1996, 486 pp. Reviewed by John W. McDonald     

Statistics: Decisions through Data

Abstract

Regression Graphics: Ideas for Studying Regressions Through Graphics by R. Dennis Cook, New York: Wiley, 1998, xviii + 349 pp. Reviewed by William G. Jacoby

Misused Statistics: Second Edition, Revised and Expanded by H.F. Spirer, L. Spirer, and A.J. Jaffe, New York: Dekker, 1998. Reviewed by Arnold Barnett     

Book reviews

Béla Martos: Nonlinear Programming. Theory and Methods. Akadémiai Kiadó, Budapest 1975, 279 S., Ft 180.

B. Krekó: Optimierung – Nichtlineare Modelle. VEB Deutscher Verlag der Wissenschafter, Berlin 1974, 508 S., 102 Abb., 48,– M.

H. Bialy, M. Obrich: Optimierung-eine Einführung mit Anwendungsbeispielen. VEB Fachbuchverlag, Leipzing 1975, 296 S., 82 Abb., 100 Beip., DM 18.

G. A. Aschincer: Stabilitätsaussagen über Klassen von Matrizen mit verschwindernden Zeilensummen. Lecture Notes in Economics and Mathematical Systems 113. Springer Verlag, Nerlin-Heidelberg-New York 1975. V, 102 S., 57 Abb., 4 Tab., DM 18.     

Diamond theorem for a finitely generated free profinite group

We extend Haran’s Diamond Theorem to closed subgroups of a finitely generated free profinite group. This gives an affirmative answer to Problem 25.4.9 of Fried and Jarden (in Field Arithmetic, 2nd edn, Springer, Berlin Heidelberg, New York, 2005).     

On the congruences of Jacobi forms

In this paper, we study congruence properties of coefficient of Jacobi forms. The result for elliptic modular form case was studied by Sturm (Lecture Notes in Mathematics, Springer, Berlin Heidelberg New York 1987).     

Dynamic crack propagation in a 2D elastic body: The out-of-plane case

Already in 1920 Griffith has formulated an energy balance criterion for quasistatic crack propagation in brittle elastic materials. Nowadays, a generalized energy balance law is used in mechanics [F. Erdogan, Crack propagation theories, in: H. Liebowitz (Ed.), Fracture, vol. 2, Academic Press, New York, 1968, pp. 498-586; L.B. Freund, Dynamic Fracture Mechanics, Cambridge Univ. Press, Cambridge, 1990; D. Gross, Bruchmechanik, Springer-Verlag, Berlin, 1996] in order to predict how a running crack will grow. We discuss this situation in a rigorous mathematical way for the out-of-plane state. This model is described by two coupled equations in the reference configuration: a two-dimensional scalar wave equation for the displacement fields in a cracked bounded domain and an ordinary differential equation for the crack position derived from the energy balance law. We handle both equations separately, assuming at first that the crack position is known. Then the weak and strong solvability of the wave equation will be studied and the crack tip singularities will be derived under the assumption that the crack is straight and moves tangentially. Using the energy balance law and the crack tip behavior of the displacement fields we finally arrive at an ordinary differential equation for the motion of the crack tip.