STABILITY ANALYSIS OF HOPFIELD NEURAL NETWORKS WITH TIME DELAY

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｒｅｃｅｎｔｙｅａｒｓｔｈｅｄｙｎａｍｉｃｂｅｈａｖｉｏｒｏｆｔｈｅｆｏｌｌｏｗｉｎｇＨｏｐｆｉｅｌｄｎｅｕｒａｌｎｅｔｗｏｒｋｓｍｏｄｅｌｗｉｔｈｔｉｍｅｄｅｌａｙｈａｖｅｂｅｅｎｉｎｖｅｓｔｉｇａｔｅｄｔｈｏｒｏｕｇｈｌｙＣｉ ｘｉ(ｔ) =-ｘｉＲｉ + ∑ｎｊ=1Ｔｉｊｆｊ(ｘｊ(ｔ-τｉｊ) ) +Ｉｉ　　 (ｉ=1 ,2 ,… ,ｎ) ,( 1 )ｗｈｅｒｅＲｉ,ＣｉａｎｄＩｉｒｅｐｒｅｓｅｎｔｒｅｓｉｓｔａｎｃｅ ,ｃａｐａｃｉｔａｎｃｅａｎｄｅｌｅｃｔｒｉｃｃｕｒｒｅｎｔ.Ｒｉ,Ｃｉａｒｅｐａ…     

Philosophy of Mathematics and Natural Science,by H. Weyl

The paper begins with a general discussion of the properties of elastic liquids and with the use of models, consisting of springs and dashpots, to describe their behaviour. Next the linear and non-linear behaviour of these liquids are described together with some of the more striking observed properties. Experimental measurements are next discussed. The paper ends with a brief account of theoretical work that has been done on elastic liquids.     

Dynamics of Self-Organized and Self-Assembled Structures,by Rashmi C. Desai and Raymond Kapral

The arrival of the first hard X-ray free electron laser facilities promises new advances in structural dynamics and nanoscale imaging that will have impact across the sciences. This introductory review is intended to cover the basic physics behind this potential and illustrate the current state-of-the-art by discussing a number of recent findings from the LCLS facility at the Stanford Linear Accelerator Centre (SLAC). We concentrate on the new science using these light sources rather than the new light source technology itself, although a brief introduction to the operation of LCLS is given. Emphasis is placed upon the new regime of high intensity X-ray matter interaction physics with ultrashort X-ray pulses. We discuss how the unique combination of X-ray parameters will open new opportunities for time resolved structural studies and how the high brightness enables a new class of coherent diffraction X-ray imaging. The potential importance of this new imaging method in the study of nanostructures and biological systems at the sub-cellular and molecular level will be outlined.     

Basics of Statistical Physics,by Harald J.W. Müller-Kirsten

Reactor Physics. By R. Schulten and W. Güth. Translated by W. K. Mansfield. In two volumes. (Harrap, 1967.) [Vol. I: pp. viii + 144; Vol. II: pp. vi+ 154.] 22s. 6d. each volume.

Principles of Atomic Spectra. By B. W. Shore and D. H. Menzel. (John Wiley, 1968.) [Pp. xiv + 538.] £8. 18s. 0d.

Les Transitions Electroniques dans les Solides Non Conducteurs. (Colloque de la Société Français de Physique.) (Presses Universitaires de la France, 1967.) [Pp. 177.] 35 F.

Mechanics. Point Objects and Particles. By Terry Triffet. (John Wiley, 1968.) [Pp. ix + 546.] 32s.

Traité ?Électricité Théorique, Vol. IV: Electromagnetism, etc. By Marc Jouguet. (Paris: Gauthier-Villars, 1968.) [Pp. 350.] 94 F.

Modern Physics: An Introductory Survey. By Arthur Beiser. (Addison-Wesley, 1968.) [Pp. ix + 221.] 26s.

Perpetual Motion: Electrons and Atoms in Crystals. By Alec T. Stewart. (Heinemann Educational Books, 1968.) [Pp. x + 146.] 25s.

An Introduction to the Theory of Superconductivity. By C. G. Kuper. (Clarendon Press: Oxford University Press, 1968.) [Pp. vii + 301.] 60s. Scope: Textbook. Level: Postgraduate; Undergraduate.

Progress in High Temperature Physics and Chemistry. Edited by C. A. Rouse. (Pergamon Press, 1968.) [Pp. 176.] 75s.

Ondes dans las Plasmas. By Daniel Quémada. (Paris: Hermann, 1968.) [Pp. 384.] 48 Fr.

Plasmas et Milieux Ionisés. By Evry Schatzman.(Presses Universitaires de la France, 1968.) [Pp. 134.] 16 Fr.

Mechanics. By R. C. Smith and P. Smith. (John Wiley &; Sons, 1968.) [Pp. xviii + 263.] 80s. Scope: Textbook. Level: Undergraduate.

Materials of High Vacuum Technology. Vol. 2: Silicates. By Werner Espe. (Pergamon Press, 1968.) [Pp xxiii + 660.] £16.

Glassblowing for Laboratory Technicians. By R. Barbour. (Pergamon Press, 1968.) [Pp XV + 245.] 40s.

Equilibrium Thermodynamics. By J. C. Adkins. (McGraw-Hill, 1968.) [Pp. xii + 283.] 48s. Scope: Textbook. Level: Undergraduate.

Introduction to Thermodynamics of Irreversible Processes. (Third Edition.) By I. Prigogigne. (John Wiley (Interscience), 1968.) [Pp. xv + 147.] 56s. Scope: Library. Level: Specialist/postgraduate.

Introduction to Physical Statistics. By Bruce R. Lindsay. (Dover Books (Constable), 1968.) [Pp. ix + 306.] 26s. 6d. Scope: Textbook. Level: Undergraduate.

Solid State Physics. An Introduction to its Theory. By H. Clark. (Macmillan, 1968.) [Pp. vii + 239.] 40s. Scope: Textbook. Level: Specialist/postgraduate.

Wave Mechanics. By Gunther Ludwig. (Pergamon Press, 1968.) [Pp. v + 230.] 30s. hard cover; 21s. flexi.

Introduction to Special Relativity. By Robert Resnick. (John Wiley, 1968.) [Pp. x + 226.] 70s.