On an integral method for backward boundary layers

Zusammenfassung Eine Integralmethode für die Lösung von zweidimensionalen Grenzschichtgleichungen wird entwickelt für Fälle, in denen die Lösungen sich anfänglich wie diejenigen von End-Grenzschichten benehmen. Diese Lösungen sind von Goldstein behandelt worden. Die bedeutendste Anwendung betrifft den Fall, wo ein zweidimensionaler Strom gegen eine Öffnung fliesst, durch welche die Flüssigkeit entleert wird. In erster Annäherung wird die Grenzschichtströmung für grosse Entfernungen von der Öffnung durch die Ähnlichkeitsgesetze der konvergenten Strömung in einem keilförmigen Kanal beschrieben. Um Strömungen dieser Art zu studieren, die über lange Entfernungen laufen, wird die Geschwindigkeit am Rande der Grenzschicht an Stelle der Entfernung längs der Grenzschicht als unabhängige Veränderliche eingeführt. Die beschriebene Methode wird auf den Fall der Strömung in Richtung eines Schlitzes angewendet, ausgehend von einem unendlichen Halbraum, ferner auf den Fall einer Strömung um eine endliche Platte, die senkrecht zur Strömungsrichtung steht. In beiden Beispielen ist die Potentialströmung in der Form des Kirchhoff-Rayleighschen Gesetzes angenommen, wobei die freien Stromlinien an die scharfen Kanten gebunden sind. Die Methode wird verallgemeinert, so dass sie für allgemeinere End-Grenzschichten benutzt werden kann. Die Resultate stimmen ausgezeichnet mit denen der Methode von Thwaites sowie mit den Ähnlichkeitslösungen von Falkner-Skan überein.     

Eigenfunctions on symmetric spaces with distribution-valued boundary forms

A characterization is given for those eigenfunctions of invariant differential operators on symmetric spaces of noncompact type which are representable as generalized Poisson integrals of distributions on the boundary, the criterion being that the function grow no faster than some power of the exponential of the distance from the origin. For symmetric spaces of arbitrary rank, the result is proved in one direction only, namely, that the Poisson integral of a distribution satisfies the growth condition; however, for rank one symmetric spaces, the converse is also shown to be true.     

IFECS—an interactive finite element computing system

The development philosophy and implementation of IFECS (an interactive finite element computing system) is described. The system, written in BASIC-PLUS for the RSTS/E computing system, provides solutions for various classes of stress problems in two dimensions. IFECS contains an automatic mesh generator, solution routines and an interactive means of interrogating the program output. This latter feature provides the user with the means of directly selecting relevant information, rather than having to wade through vast reams of the total output. The system, which may be implemented on a very simple computing configuration, is very easy to use and for many problems reduces the effective solution time to a few hours.     

The numerical simulation of multiphase flow through a porous medium and its application to reservoir engineering

The analysis of multiphase flow in porous media is of considerable significance in the field of petroleum reservoir simulation, where accurate predictions of fluid flow are important in assessing the performance of oil and gas fields. The specific case of two-phase immiscible flow is considered by first deriving the governing nonlinear partial differential equations. The space discretization is then carried out making use of the additional versatility of the finite element method compared with originally used finite differences. By using a pair of dependent variables P and R, the bandwidth of the discrete space-continuous time equations may be reduced to increase significantly the speed of the algorithm. A discussion of time-stepping methods is followed by an application of the technique to a five-spot,an extraction pattern used in the field. The boundary conditions used to simulate this flow pattern are also discussed.     

Regularity of flat free boundaries in two-phase problems for the p-Laplace operator

In this paper we continue the study in Lewis and Nyström (2010) [19], concerning the regularity of the free boundary in a general two-phase free boundary problem for the p-Laplace operator, by proving regularity of the free boundary assuming that the free boundary is close to a Lipschitz graph.     

Relativity,Gravitation and Cosmology,by Robert J.A. Lambourne

Physique des Particules. Edited by C. de Witt and C. Itzykson. (Gordon and Breech, 1973.) [Pp. xvi+537.] £13.55. Scope: Summer school lectures. Level: Specialist/post-graduate.

Colour Centres and Imperfections in Insulators and Semiconductors. By P. D. Townsend and J. C. Kelly. (Sussex University Press, 1973.) [Pp. vii + 229.] Hard £5.00; paper £3.00. Scope: Textbook. Level: Specialist/post-graduate; undergraduate (fina1 year).

The Physics of Elementary Particles. By L. J. Tassie. (Longmans, 1973.) [Pp. xi+255.] £2.95. Scope: Textbook. Level: Undergraduate.

Particles and Nuclei. Vol. 1, Part 1. By N. N. Bogolyubov. (Plenum Press, 1972.) [Pp. 189.] $46. Scope: Library. Level: For specialists only.

Particles and Nuclei. Vol. 2. By N. N. Bogulyubov. (Plenum Press, 1972.) [Pp. 309.] $92.00. Scope: Library. Level: For specialists only.

The Large Scale Structure of Space-Time. By S. W. Hawking and G. F. R. ELLIS. (Cambridge University Press 1973). [Pp. xi+391.] £10.00. Scope: Treatise/Textbook. Level: Specialist/post-graduate.

General Physics Workbook. (Physics Problems and how to solve them.) By Foster Strong. (W. H. Freeman and Son, San Franciso, Oct, 1972.) [pp. 502.] £2.50. Scope: Textbook. Level: Undergraduate; School.

Planck's Original Papera in Quantum Physics. Edited by Hans Kangro. (Taylor and Francis, 1972.) [Pp. viii+ 60.] 75p. Scope: Textbook. Level: Undergraduate.

Quantum Physics and Ordinary Language. By T. Bergstein. (Macmillan, 1972.) [Pp. xii+ 81.] £3.00. Scope: Treatise. Level: General reader.

The Use of the Scanning Electron Microscope. By J. W. S. Hearle, J. T. Sparrow and P. M. Cross. (Pergamon, 1972.) [Pp. xi+278.] £8.80. Scope: Survey. Level: Specialist/post-graduate.

Defects in Crystalline Solids. By B. Henderson. (Arnold, 1972.) [Pp. ix+203.] Cloth £6.00; Paper £3.00. Scope: Textbook. Level: Undergraduate.

An Introduction to Lattice Dynamics. By A. K. Ghatak and L. S. Khothari. (Addison-Wesley, 1972.) [Pp. vi+234.] $11.50. Scope: Textbook. Level: Post-graduate.

Case Studies in Atomic Collision Physics (2). Editors E. W. McDaniel and M. R. C. McDowell. (North-Holland, 1972.) [Pp. xiv+649.] Hfl 150.00, $47.00. Scope: Treatise/Textbook. Level: Specialist/post-graduate.

Theory of Seismic Head Waves. By V. Cerveny and R. Ravindra. (University of Toronto Press, London; Oxford University Press, 1972.) [Pp. xvi + 312.] £8.75. Scope: Treatise/textbook. Level: Specialist/postgraduate.

An Introduction to the Ionosphere and Magnetosphere. By J. A. Ratcliffe. (Cambridge University Press, 1972.) [Pp. x + 256.] £4.00. Scope: Textbook; library. Level: Postgraduate; undergraduate; school.

Optics. By C. S. Williams and A. Becklund. (John Wiley, 1972.) [Pp. xiv+397.] £7.50. Scope: Textbook; library (reference). Level: For specialists only; specialist.

Principles of Activation Analysis. By Paul Kruger. (John Wiley &; Sons Ltd., 1971.) [Pp. xi+522.] £11.75. Scope: Treatise/Textbook. Level: Undergraduate.

Colloidal and Morphological Behaviour of Block and Graft Polymers. Edited by G. E. Molau. (Plenum Press, 1971.) [Pp. xvi+ 327.] $14.50.

Spin and Isospin. By P. A. Carruthers. (Gordon &; Breach. 1971.) [Pp. ix+288.] £8.10 Scope: Textbook; library (reference). Level: For specialists only; specialist/postgraduate.

Nuclear Reactions and Nuclear Structure. By P. E. Hodgson. (Clarendon Press: Oxford University Press, 1971.) [Pp. xi+661.] £14.50. Scope: Treatise/textbook. Level: Specialist/postgraduate.

Magnetic Resonance in Metals. By J. Winter. (Clarendon Press: Oxford University Press; 1971.) [Pp. xiii+205.] £5.50.

Concepts of Atomic Physics. By D. A. Jackson. (McGraw-Hill, 1971.) [Pp. 170.] £2.50. Scope: Textbook. Level: Undergraduate.

An Introduction to the Theory of Atomic Spectra. By I. I. Sobel'Man, translated by T. F. L. LeVierge, and edited by G.K.Woodgate. (Pergamon Press, 1972.) [Pp. xvi+ 609.] £18.00. Scope: Textbook; library (reference). Level: Specialist/postgraduate.

The Jahn-Teller Effect in Molecules and Crystals. By R. Englman. (Wiley-Interscience, 1972.) [Pp. xx+ 350.] £8.00. Scope: Treatise. Level: For specialists only.

Algebraic Methods in Statistical Mechanics and Quantum Field Theory. By G. G. Emch. (Wiley-Interscience, 1972.) [Pp. xiv+ 333.] £7.85. Scope: Textbook. Level: For specialists only.

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Group Theory and the Coulomb Problem. By M. J. Englefield. (John Wiley, 1972.) [Pp. viii+ 120.] £4.75. Scope: Textbook. Level: Postgraduate.

Statistical Properties of Nuclei. Edited by J. B. Garg. (Plenum Press, 1972,) [Pp. xxiv+ 665.] $37.00. Scope: Conference Proceedings. Level: For specialists only.

Theoretical Solid State Physics. (Volume 1). By A. Haug. (Pergamon. 1972.) [Pp. xiv+ 497.] £7.00. Scope: Textbook. Level: Postgraduate; undergraduate.

Analytic Properties of Feynmn Diagrams in Quantum Field Theory. By I. T. Todorov. (Pergamon, 1971.) [Pp. xvi+ 152.] £3.75. Scope: Treatise. Level: For specialists only.

Progress in Solid State Chemistry, Vol. 7. Edited by H. Reiss and J. O. McCaldin. (Pergamon Press, 1972.) [Pp. xi+275.] £10.00. Scope: Survey. Level: Specialist/post-graduate.

Introduction to Particle Physics. By R. Omn$eGs. (John Wiley, 1971.) [Pp. xiii+ 414.] £6.00. Scope: Textbook. Level: Postgraduate.

Plasma, the Fourth State of Matter. By D. A. Frank-Kamenetskii. (Plenum Press, 1972.) [Pp. viii+ 159.] $14.00. Scope: Treatise. Level: Undergraduate.

Computer Aided Design. (Institution of Electrical Engineers, 1972.) [Pp. viii+ 431.] £11.90.

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Introduction to the Principles of Electromagnetism. By W. Hauser. (Addison-Wesley, 1971.) [Pp. xiv+ 623.] £7.00. Scope: Textbook. Level: Postgraduate; undergraduate.

Dynamica, Electricity and Magnetism. By E. W. Laing and W. McFarlane. (Oliver and Boyd, 1972.) [Pp. vii+ 156.] £1.75. Scope: Textbook. Level: Undergraduate.

Nineteenth Century Aether Theories. By K. F. Schaffner. (Pergamon, printed in Hungary, 1972.) [Pp. ix+ 278.] £3.25. Scope: Textbook; survey. Level: General reader; undergraduate.

Mechanics and Electrodynamics. By L. D. Landau and E. M. Lifshitz. (Pergamon. 1972.) [Pp. xiii+ 282.] £3.00. Scope: Textbook. Level: Postgraduate; undergraduate.

Theory of the Unmagnetized Plasma. By D. C. Montgomery. (Gordon and Breach, 1971.) [Pp. 416.] £7.30, Scope: Treatise. Level: Specialist/postgraduate.

Amorphous Materials. Edited by R. W. Douglas and B. Ellis. (Wiley-Interscience, 1972.) [Pp. xviii+ 550.] £9.00. Scope: Conference proceedings; survey; library. Level: For specialists only; specialist/postgraduate.     

A Helly-Type Theorem for Line Transversals to Disjoint Unit Balls

   Abstract. Let F be a family of disjoint unit balls in R ³ . We prove that there is a Helly-number n ₀ ≤ 46 , such that if every n ₀ members of F ( | F | ≥ n ₀ ) have a line transversal, then F has a line transversal. In order to prove this we prove that if the members of F can be ordered in a way such that every 12 members of F are met by a line consistent with the ordering, then F has a line transversal. The proof also uses the recent result on geometric permutations for disjoint unit balls by Katchalski, Suri, and Zhou.     

A local–global principle for algebras with involution and hermitian forms

 Weakly hyperbolic involutions are introduced and a proof is given of the following local–global principle: a central simple algebra with involution of any kind is weakly hyperbolic if and only if its signature is zero for all orderings of the ground field. Also, the order of a weakly hyperbolic algebra with involution is a power of two, this being a direct consequence of a result of Scharlau. As a corollary an analogue of Pfister's local–global principle is obtained for the Witt group of hermitian forms over an algebra with involution. Received: 29 October 2001; in final form: 9 August 2002 / Published online: 16 May 2003 Mathematics Subject Classification (2000): 16K20, 11E39