The subject of Galaxy Formation has advanced considerably during the past decade. On the theoretical side two theories in particular have been developed to the point where confrontation with observation will be possible; these are the "Gravitational Instability Picture" and the "Cosmic Turbulence Theory." These theories are discussed at some length here, with particular attention to the question of the origin of cosmic angular momentum and the nature of the initial conditions. There is now a considerable body of data on galaxies; the problem is in deciding which kind of observation is most relevant to understanding the origin of galaxies. Throughout the review an attempt is made both to put the present research in its historical perspective and to stress the possibilities for future advances towards the goal of understanding the origin of cosmic structure.

We present here a survey on the progress of nonlinear optics in recent years. Emphasis is on physical ideas, basic principles, and important experimental results.

A NATO Advanced Studies Institute on the Origins and Abundances of the Chemical Elements was held at the Institute of Astronomy, Cambridge, England from 23 July to 9 August 1974. The problems discussed there are the basis for this review. Three major areas can be identified. First, the normal distribution of chemical and isotopic abundances and deviations from it must be determined observationally. Second, the relevant nuclear processes and their sites and products must be identified. Third, a model of the evolution of galaxies which includes the relevant processes and produces the observed abundances must be formulated. There has been rapid progress recently in all three of these areas.

The purpose of this review article is to explain and illustrate in detail the technique of dimensional regularization, which is a major mathematical tool in the renormalization program of gauge theories. The most important single feature of the new technique is the concept of analytic continuation in the number of space-time dimensions $2\omega$, where the regulating parameter $\omega$ is complex in general, and $\omega =2\mathrm{}$ corresponds to four-dimensional space-time. The technique of dimensional regularization preserves the local gauge symmetry of the underlying Lagrangian and thereby permits a consistent gauge-invariant treatment of divergent Feynman integrals to all orders in perturbation theory. The method can thus be applied—as demonstrated in this article—not only to Abelian gauge models, but more importantly to non-Abelian theories such as Yang-Mills fields and quantum gravity, to which the majority of conventional regularization procedures is inapplicable. We illustrate both the advantages and the limitation of dimensional regularization, as well as its extension to massless particles.

The Proudman-Taylor theorem states that, in a fluid rotating steadily about a vertical axis, if a flow pattern is induced—for example by the slow steady motion of a solid body such as a squat cylinder at one level—the same flow pattern is induced at all levels by Coriolis forces. The steady equilibrium situation is simply understood in terms of a balance of the horizontal Coriolis forces at all levels. The mechanism providing the accelerations whereby the equilibrium is established is shown in various examples to involve vertical transport of momentum by flow around loops linking the various levels. The limited role of this mechanism in atmospheric circulation, in the dynamo action in the earth's fluid core responsible for terrestrial magnetism, and in the liquid-drop model of nuclear rotation is briefly discussed.

This review covers several topics involving renormalization group ideas. The solution of the $s$-wave Kondo Hamiltonian, describing a single magnetic impurity in a nonmagnetic metal, is explained in detail. See Secs. VII-IX. "Block spin" methods, applied to the two dimensional Ising model, are explained in Sec. VI. The first three sections give a relatively short review of basic renormalization group ideas, mainly in the context of critical phenomena. The relationship of the modern renormalization group to the older problems of divergences in statistical mechanics and field theory and field theoretic renormalization is discussed in Sec. IV. In Sec. V the special case of "marginal variables" is discussed in detail, along with the relationship of the modern renormalization group to its original formulation by Gell-Mann and Low and others.

Photoneutron cross-section data obtained with monoenergetic photon beams are presented, many of them in graphical form in a uniform format. Tables of values for quantities derived directly from the data, such as integrated cross sections, and for quantities derived indirectly from the data, such as parameters of Lorentz curves fitted to the data, are presented as well. Average properties of the giant dipole resonance obtained from the data are compared with theory, as are more general nuclear quantities, such as symmetry energies, deformations, and level-density parameters. Structure in the cross sections and various other special topics are discussed, and a survey and a critique of the experimental techniques used to obtain the data are included.

The field of electroexcitation of nuclear M1 transitions is reviewed. The subject is introduced with an elementary description of the relationship between backward-angle electron scattering and M1 excitation. Data analysis methods as well as 180° electron scattering techniques are also treated. The discussion of experimental results emphasizes the strength of the spin-flip transition, the concentration of M1 strength in self-conjugate nuclei, the degree of fragmentation of this strength in other nuclei, the response of odd-$A$ rotational nuclei to 180° electron scattering, and the possible existence of an M1 giant resonance among the nuclides, especially the heavy nuclei.

Quasielastic collisions between complex nuclei, elastic, inelastic, and few-nucleon transfer are discussed both as a classical and quantal process. The classical trajectories can be used to illuminate the dependence of the quantal calculations on the physical parameters, and indeed can be used in a predictive way to suggest under what circumstances ambiguities can be resolved. The $S$-matrices for various quasielastic processes are exhibited and the quantal analog of the classical deflection function is compared with the classical one. The smooth behavior of the $S$-matrix for large angular momentum $l$ suggests the possibility of a two-part approach where the lower $l$ region is computed quantum mechanically, and the high-$l$ region is either parametrized, treated semiclassically, or interpolated between widely spaced $l$'s. The much greater sensitivity of several-nucleon transfer reactions to the interior region compared to elastic and inelastic scattering is stressed. Various aspects of two-nucleon transfer are discussed, including multiple-step processes, their dependence upon collectivity of the intermediate states, and the opposite sense of the interference involved in pickup and stripping reactions to vibrational states.

The physical mechanisms important to the operation of tunable lasers utilizing organic dyes are discussed. The uniqueness of organic dyes as a tunable laser medium is reviewed by investigating the optical properties of two broadened energy levels. The complete energy level system is investigated and gain and efficiency are calculated. The wide variety of practical laser configurations possible for optically pumped dye lasere are examined. New topics of interest such as dye vapor lasers and short pulse generation are discussed.

Structural instabilities are now being found in many high-temperature superconductors. Compounds with the A-15 ($\beta$-W) structure comprise the most important group of these materials, and their properties have been extensively studied for over 15 years. A review is given of some of these results, particularly those relating to the elastic behavior. The empirical relation of the structural instability and the anharmonicity to the high superconducting transition temperature is discussed.

We investigate the hypothesis that diffractive scattering is dominated (as $s\to \infty$) by a Pomeron Regge pole [${\alpha }_P\mathrm{}\left(t\right)\mathrm{}$]. This hypothesis is particularly attractive since a Regge pole and its attendant cuts satisfy $t$-channel unitarity. For a complete theory the constraints of $s$-channel unitarity must also be satisfied. In addition to Froissart's bound and its wellknown consequence, ${\alpha }_P\mathrm{}\left(0\right)\mathrm{}\le 1$, $s$-channel unitarity implies a large number of decoupling theorems for an isolated Pomeron pole with ${\alpha }_P\mathrm{}\left(0\right)=1\mathrm{}$. Here we systematically review these decoupling theorems. The theorems are treated in order of increasing strength so as to clearly distinguish the "strong theorems" which can be used to prove the complete decoupling of the Pomeron (e.g., ${\sigma }_{\mathrm{Tot}}\to 0$) from the "weak theorems" which cannot. This review is undertaken with two goals in view: (1) To focus attention on possible points of departure for more realistic treatments of diffractive scattering, and (2) to emphasize the importance of $s$-channel unitarity which is expected to strongly constrain diffractive production in certain regions of phase space regardless of the exact nature of the Pomeron singularity.

Graded Lie algebras have recently become a topic of interest in physics in the context of "supersymmetries," relating particles of differing statistics. In mathematics, graded Lie algebras have been known for some time in the context of deformation theory. In this paper we discuss basic properties of graded Lie algebras and present various new constructs for producing examples of such algebras. In addition we present a short survey of the role played by graded Lie algebras in mathematics and review in some detail the recent applications of supersymmetry in the physics of particles and fields.

This supplement to the 1974 edition of "Review of Particle Properties," Particle Data Group [Phys. Lett. 50B, No. 1 (1974)], contains an announcement concerning the postponement of the usual Review, a list of Errata, and a tabulation of the experimental results on the newly discovered mesons.

The "action potential" is a pulselike voltage wave which carries information along a nerve fiber. Starting with fundamental concepts of biochemistry and electromagnetic theory, the derivation of the nonlinear diffusion equation which governs propagation of the action potential is reviewed. Our current understanding of this equation is discussed, paying particular attention to questions of interest in physics and applied mathematics.