Benzenoid Molecules with Uniform Distribution of π-Electrons within Rings

In a recent work it was demonstrated that in linear hexagonal chains the distribution of π-electrons into rings (as computed by means of the Randić–Balaban method) is uniform, irrespective of the nature of the terminal fragments. We now establish that an analogous, yet somewhat more complex, uniformity in the π-electron distribution exists also in double linear hexagonal chains, as well as in some other benzenoid systems.     

Dependence of the S-matrix on the choice of field variables in the effective Lagrangian

The dependence of the on-shellS-matrix on the change of the Lagrangian induced by a nonlinear substitutionF() is investigated by means of a graphical analysis. A cancellation mechanism is found and used to show that the tree approximation of theS-matrix is independent of such a substitution and that the Jacobian of the substitution has to be introduced in order to cancel a new class of singular one-loop graphs and to recover the primaryS-matrix at the one-loop level.     

Diagrams,orientations, and varieties

One of the central problems in the theory of ordered sets is to describe the orientations of the covering graph of an ordered set. We show that the particular operation called inversion, together with the classical constructions of retraction and product, provide a context for the classification of all such orientations. AMS subject classifications (1980). 06A10, 05C75, 05C20.     

Linear mode conversion of waves near the maxima or minima of the density in a warm magnetized plasma

Behaviour of the h. f. electrostatic waves near the plasma or upper hybrid resonances was studied in the case that these resonances are situated at the maxima or minima of the plasma density. Supposing the parabolic density profile in these regions we obtained the connection formulae for the WKB solutions. In a weakly inhomogeneous magnetoplasma the effect of the parabolic profile manifests itself only in narrow frequency band centred at the resonance frequency corresponding to the extreme value of the density. The whole process can be then described by only two coefficients, viz. the power conversion and power transmission coefficients.     

Excitation functions for some output channels following the p +55Mn interaction atE p=1·3–2·0 MeV

Excitation functions for the⁵⁵Mn(p, p )⁵⁵Mn,⁵⁵Mn(p, n )⁵⁵Fe and⁵⁵Mn(p, )⁵⁶Fe reactions are studied for proton beam energyE _p=1·3–2 MeV. The excitation functions are established from yield functions for -rays emitted from the first excited states of final nuclei. Many resonances are observed and competition of their decay into all three output channels is analysed. Spin-parity assignment for some resonant states in the⁵⁶Fe compound nucleus is deduced.Participated partly in the course of his work on a Thesis.The authors wish to thank the staff of the Van de Graaff accelerator at Charles University in Prague for the efficient operation of the machine and dr. I. Wilhelm for the valuable technical help in the early period of the experimental work. One of us (N. A. N.) acknowledges the staff of the Dept. of Nuclear Physics of Charles University in Prague for the excellent working conditions.     

Character formulas for some classes of atypical gl(m+nε)- and p(m)-modules

If p is an arbitrary parabolic subsuperalgebra of g = gl(m + n), p(m), a character formula for the generic finite-dimensional irreducible g-module, such that p is the stabilizer of its lowest weight space, is announced. Furthermore, an estimate for the character of any finite-dimensional irreducible g-module in terms of its highest weight with respect to a distinguished Borel subsuperalgebra is presented (inequality (4)) and a sufficient condition for this to be an equality is found. In this way, two generalizations of the Kac character formula for typical modules are obtained: a formula concerning an arbitrary Borel subsuperalgebra ((1)) and a more effective formula ((3)) for the special case of a distinguished Borel subsuperalgebra. The complete proofs will appear in [14].Partially supported by Contract 911/11.04.88 with the Bulgarian Ministry of Culture, Science, and Education.     

On stability of Raman and degenerate hyper-Raman scattering

The problem of the stationary generation by Raman and degenerate hyper-Raman scattering is solved by means of two methods: stationary solution of the generalized Fokker-Planck equation and linear analysis of stability of the Langevin equations. The conditions of stability and the corresponding stationary values for amplitudes of the Stokes, anti-Stokes or output laser modes are obtained for particular cases. A phenomenon analogous to the second order phase transition can occur for Stokes or anti-Stokes interaction of Raman scattering above the threshold value of the pump amplitude. The anti-Stokes interaction of degenerate hyper-Raman scattering can show bistable behaviour above the second threshold value of the pump amplitude.The author would like to express his sincere thanks to Dr. J. Peina for comments and stimulating discussions.     

On FMR modes in bubble domain lattices

Two solutions of the problem of non-uniform ferromagnetic resonance in a hexagonal bubble domain lattice are presented under the simplifying assumption of lattice period much smaller than the film thickness. Fine divisions of the lattice cell into supposedly uniform subdomains render sets of linear equations for the local amplitudes which are solved numerically. Analytical solution of the time-dependent magnetostatic (Walker-mode) problem is obtained by expansion in simple elliptic functions similar to that suggested by Sigal. The results support, respectively, the interpretation of FMR experiments derived by Klem and Kaczér from a crude (minimal) subdivision of the elementary cell, and the three-mode dipolar-field model recently proposed by the author on a largely intuitive basis.     

Dynamics of intense Langmuir waves in current-carrying plasmas

Basic equations including ponderomotive effects of Langmuir waves in a current-carrying plasma are presented. In such a system, dynamics of an initially monochromatic plasma wave is investigated both analytically and numerically. Various regimes of developed modified decay and modulational instabilities of the wave are modelled by using a macroparticle numerical code. In this way the cooperative nature of both ponderomotive and drift effects supporting plasma heating is demonstrated. The underlying physical processes are discussed and relation to the solar flare theory is suggested.Dedicated to Academician Václav Votruba on the occasion of his eightieth birthday.It is pleasure to acknowledge the staff members of the Computational Centre at Ondejov for their kind support in performing the numerical computations.