Table of contents

A generalized theory of angular momenta has been developed over the past few years. The new results account for a substantial change in the role played by Clebsch-Gordan coefficients both in physical and in mathematical problems. This review considers two aspects of the theory of Clebsch-Gordan coefficients, which forms a part of applied group theory. First, the close relation of these coefficients with combinatorics, finite differences, special functions, complex angular momenta, projective and multidimensional geometry, topology and several other branches of mathematics are investigated. In these branches the Clebsch-Gordan coefficients manifest themselves as some new universal calculus, exceeding substantially the original framework of angular momentum theory. Second, new possibilities of applications of the Clebsch-Gordan coefficients in physics are considered. Relations between physical symmetries are studied by means of the generalized angular momentum theory which is an adequate formalism for the investigation of complicated physical systems (atoms, nuclei, molecules, hadrons, radiation); thus, e.g., it is shown how this theory can be applied to elementary particle symmetries. A brief summary of results on Clebsch-Gordan coefficients for compact groups is given in the Appendix.

A review is given of the theory of the generation of ultrashort light pulses in lasers with bleachable filters. Attention is mainly concentrated on the statistical aspects of the formation of ultrashort light pulses in such lasers. The topics discussed include the formation of laser modes, the narrowing of the spectrum in the stage before the bleaching of the filter, the transformation of the field profile during the bleaching process, the statistics of the appearance of single ultrashort pulses, and the influence of the gain saturation on the time characteristics of the radiation. Several additional effects, which influence the final structure of the radiation, are considered. A quantitative theory is given of the widely used two-photon method for measuring ultrashort pulses and a basic shortcoming of this method is pointed out: it is not possible to find whether one or many pulses appear in a given period.

TABLE OF CONTENTS Introduction 45 1. Endurance of Solids under Load and the Fundamental Premises of the Kinetic Conception of Strength 46 2. Study of the Process of Failure of Materials by Direct Physical Methods 50 3. Cases of Complicated Failure 58 4. Some Problems in the Development of Kinetic Ideas on the Failure Process 59 5. Kinetic Theories of Failure 60 6. Conclusion 60 Bibliography 61

The review is devoted to a description of the possibilities afforded by transmission electron microscopy for the investigation of magnetic structures of thin ferromagnetic films, and presents experimental data on magnetic films obtained by using a transmission electron microscope. We consider and compare different microscope operating regimes for observing the magnetic structure. The formation of the contrast of the magnetic structures in the most widely used modes, namely the defocusing mode and the small-angle electron diffraction mode, are considered in detail. Particular attention is paid to obtaining data on the domain walls and the fine structure of the magnetization inside the domains. Different methods of measuring the widths of the boundaries are compared, and the possible sources of errors are discussed. The prospects for using ultra-high voltage electron microscopes for the investigation of thicker films are noted. Experimental data are given on the investigation of domain configurations in single-crystal foils and in polycrystalline films, and the dependences of the magnetic parameters of the film on the structure and on the conditions of obtaining the films are discussed. Results of an investigation of a quasistatic and pulsed remagnetization of magnetic films are described.

A review is presented of theoretical and experimental results of an investigation of natural fluctuations in gas and solid-state lasers. All the known theoretical results are obtained by a single method based on the equations of the quasiclassical laser theory. In the calculation of the fluctuations, the equations for the amplitudes and phases of the field are regarded as Langevin equations with suitably introduced fluctuation sources. The sources of the thermal fluctuations of the resonator are determined by the Kallen-Welton formula. The sources of the non-equilibrium fluctuations of the polarization of the working medium are calculated on the basis of the equations for the density-matrix elements. The fluctuations of the amplitudes and phases in linear and ring lasers are considered under arbitrary pump-to-threshold ratios. The natural line width of the laser radiation is calculated. The coupling of opposing waves in a ring laser, due to scattering by the mirrors, is taken into account. The maximum sensitivity of a laser gyroscope is estimated. The results of the theory are compared with the experimental data. A brief description of the status of the problem of calculating the natural fluctuations in lasers and an estimate of the possibilities of the quasiclassical method of calculating fluctuations are given in the conclusion.