Self-dual Yang-Mills fields ind=4 and integrable systems in 1≤d≤3

The Ward correspondence between self-dual Yang-Mills fields and holomorphic vector bundles is used to develop a method for reducing the Lax pair for the self-duality equations of the Yang-Mills model ind=4 with respect to the action of continuous symmetry groups. It is well known that reductions of the self-duality equations lead to systems of nonlinear differential equations in dimension 1d3. For the integration of the reduced equations, it is necessary to find a Lax pair whose compatibility conditions is these equations. The method makes it possible to obtain systematically a Lax representation for the reduced self-duality equations. This is illustrated by a large number of examples.N. N. Bogolyubov Theoretical Physics Laboratory, JINR, 141980 Dubna, Russia. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 102, No. 3, pp. 384–419, March, 1995.     

Boundary-value problem for the two-dimensional stationary heisenberg magnet with nontrivial background. II

The investigation of the boundary-value problem on a half-plane for the two-dimensional stationary Heisenberg magnet is continued. The asymptotic behavior of N-soliton solutions is discussed. The asymptotic contribution of the continuous spectrum is calculated. The gauge equivalence of the boundary-value problems for the models of a magnet and the elliptic equation represented by the sinh—Gordon equation is considered.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 104, No. 3, pp. 513–529, September, 1995.     

A Ramification Formula for Poincare Series, and a Hyperplane Formula for Modular Invariants

Let (A) be the coefficient of the second term in the Laurentexpansion about T 1 of the Poincare series p(A, t) of a gradedring A. For a finite extension of integrally closed domains,we prove a formula relating if (B), if (A) and the differentialexponent of B over A. As an application, we prove a conjectureof Carlisle and Kropholler which computes for rings of modularinvariants of finite groups in terms of stabilizers of hyperplanes.     

On some boundary value problems with integral conditions for functional differential equations

For the functional differential equationu ⁽ⁿ⁾ (t)=f(u)(t) we have established the sufficient conditions for solvability and unique solvability of the boundary value problems $$u^{(i)} (0) = c_i (i = 0,...,m - 1), \smallint _0^{ + \infty } |u^{(m)} (t)|^2 dt< + \infty $$ and $$\begin{gathered} u^{(i)} (0) = c_i (i = 0),...,m - 1, \hfill \\ \smallint _0^{ + \infty } t^{2j} |u^{(j)} (t)|^2 dt< + \infty (j = 0,...,m), \hfill \\ \end{gathered} $$ wheren≥2,m is the integer part of $\tfrac{n}{2}$ ,c _i ∈R, andf is the continuous operator acting from the space of (n?1)-times continuously differentiable functions given on an interval [0,+∞] into the space of locally Lebesgue integrable functions.     

Polarised structure functions

This talk discusses the current understanding in some aspects of polarised lepton-nucleon deep inelastic scattering. The first section focuses on the non-singlet part of available spin dependent structure function data. The results, though consistent with theoretical predictions in this sector, are extremely sensitive to extrapolation of the data to thex→1 region and seem to indicate that the quarksdo carry a very small fraction of the nucleon spin. We then review the formalism of DIS processes with emphasis on the gluon sector.     

Pseudo goldstones at future colliders from the extended BESS model

Decays and branching ratios of light neutralino production in $Z_R^0 \to \tilde \chi _i^0 \tilde \chi _j^0 $ in the left-right super-symmetric model are considered. We study in detail the signatures of one and two sided events in $Z_R^0 \to \tilde \chi _1^0 \tilde \chi _2^0 $ and $Z_R^0 \to \tilde \chi _2^0 \tilde \chi _2^0 $ respectively, and their dependence on the parameters of the light neutralino mixing matrix.     

Vibrational Population of Hydrogen Molecules Excited by an RF Discharge in an Expanding Thermal Arc Plasma as Determined by Emission Spectroscopy

This work is devoted to the determination of the vibrational population of hydrogen molecules in the ground and excited electronic states from the analysis of visible spectra of the H₂ molecules excited by an RF discharge in an expanding thermal arc plasma. Comparison of the experimental results on relative electron-impact excitation cross sections for the transition H₂(X¹Σ, υ⁰ = 0)→ H₂(d³II_u, υ′) with other experiments, and with calculations based on the Franck-Condon principle, shows good agreement. This means, that for plasma under investigation: 1) in the ground electronic state H₂(d³II_u,υ′), only the lowest vibrational level with υ⁰ = 0 is significantly populated, and 2) direct electron exictation of H₂(d³II_u, υ′, υ′) state from the ground state H₂(X¹Σ, υ⁰ = 0) dominates.     

CW diode pumping and FM mode locking of a Nd: KGW laser

We have demonstrated cw diode end pumping of Nd: KGW, a novel solid-state gain medium, with up to 30% conversion efficiency into near-TEM₀₀ (M² < 1.05) output at = 1.067 µm for a pump level of 2.7 W. The slope efficiency was limited by intracavity reflections to 36%; however, direct comparison to a similar Nd:YAG laser indicates the same intrinsic slope efficiency of 60%. FM mode locking of this laser at 200 MHz has produced 12 ps pulses (compared to 16 ps for Nd: YAG), although an intracavity etalon was required. Considerable reduction in pulse width is possible (the line width limit is 0.5 ps) but different techniques may be necessary. Spatial hole burning was evident in both the 120 GHz free-running spectrum and the etalon-limited mode-locked spectrum.     

The nonlinear decay of complex signals in dissipative media

The solution of Burgers' equation with random initial conditions is often said to describe "Burgers turbulence." The Burgers equation describes two fundamental effects characteristic of any turbulence-the nonlinear transfer of energy over the spectrum and the dissipation of energy in the small-scale components. Strong interaction between coherent harmonics, associated with the nondispersive nature of the dynamics, leads to the appearance of local self-similar structure. In Burgers' equation, continuous random initial fields are transformed into sequences of regions with regular behavior, with random locations of the shocks separating them. Moreover, the statistical properties of such random fields are also self-similar. It is already known that the merging of the shocks leads to an increase of the external scale of the turbulence, and because of this the energy of a random signal ("noise") decreases more slowly than the energy of simple signals. Here we show that similar behavior takes place for complex regular signals with fractal structure in the coordinate or in the wave-number space. In all these cases, the law of increase of the external scale is determined by the behavior of the structure function of the integral of the initial field-i.e., the structure function of the initial action. (c) 1995 American Institute of Physics.