Angular eikonal of a conicoid

Exact formulas for the angular eikonal of decentered and oblique conicoids are obtained based on the analysis of the properties of conicoids and angular eikonals. The case of a paraboloid is considered separately. Exact formulas for the angular eikonal open the possibility of construction of an exact theory of aberrations.     

On irreversibility of von Neumann additive cellular automata on grids

The von Neumann cellular automaton appears in many different settings in Operations Research varying from applications in Formal Languages to Biology. One of the major questions related to it is to find a general condition for irreversibility of a class of two-dimensional cellular automata on square grids (σ⁺-automata). This question is partially answered here with the proposal of a sufficient condition for the irreversibility of σ⁺-automata.     

Exact solutions inU 4 gravity. I. The ansatz for self double dual curvature

We investigate the energy-momentum and spin field equations of gravity theory on a Riemann-Cartan space-time (including metric and torsion,U ₄-manifold). The structure of the rather complicated nonlinear differential equations of second order is made considerably easier to survey by decomposing curvature into its self and anti-self double dual parts. This leads to an obvious ansatz for the self double dual curvature, whereby the field equations are reduced to Einstein's equations with cosmological term. To solve the double dual ansatz, we choose proper variables adopted to its double duality, and perform a (3+1)-decomposition of exterior calculus. We examine these equations further on a Kerr background with cosmological constant for the Riemannian geometry.     

High-pressure effect on the crystal and magnetic structure of LuMnO3: Correlation between a distortion of the triangular lattice and the symmetry of the magnetic state in hexagonal frustrated manganites

The effect of a high pressure (up to 6 GPa) on the crystal and magnetic structure of the hexagonal manganite LuMnO₃ is studied by neutron diffraction in the temperature range 10–295 K. It is found that, as the pressure increases, the ordered magnetic moment of Mn ions at T = 10 K decreases noticeably from 2.48 (0 GPa) to 1.98 μ_B (6 GPa). This decrease is due to an enhancement of the geometrical frustration effects on the triangular lattice. At the same time, the symmetry of the triangular antiferromagnetic state (the irreducible representation Γ₂) remains unchanged. A correlation is revealed between the distortion parameter of the triangular lattice formed by Mn ions and the symmetry of the antiferromagnetic state of hexagonal manganites RMnO₃. Based on this correlation, a generalized magnetic phase diagram of these compounds is constructed. The obtained phase diagram provides an explanation for the changes observed in the magnetic state of hexagonal manganites caused by high pressure and chemical substitution.     

Algorithm for nonlinear digital filtering of harmonic filling of phase-shift keyed signals

In this work, we propose a method for nonlinear digital filtering of phase-shift keyed signals with different carrier frequencies on the basis of separating the phase discontinuities of the input signals. The method allows one to avoid compensation for unknown frequency shift in the problems of determining the time delay of signals in the case of multichannel propagation. The efficiency of the proposed method is shown for the signals which are short informative packages with the phase-shift keying against the noise background in the presence of the Doppler effect. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 8, pp. 704–711, August 2006.     

The measurement of beta asymmetries at UNISOR/NOF using external plastic scintillator detectors

The performance of two external plastic scintillator detectors has been tested in an off-line mode using a source of¹⁰⁶RuFe at UNISOR/NOF. The measurement of beta asymmetries at various temperatures has resulted in the reproduction of the previously-determined magnetic dipole moment for the 1⁺ ground state of¹⁰⁶Rh and in addition the conclusion that the sign of this moment is positive.     

Extended non-abelian gauge symmetries in the classical WZNW model

Higher spin extensions of the non-Abelian gauge symmetries for the classical WZNW model are considered. Both linear and nonlinear realizations of the extended affine Kac-Moody algebra are obtained. It is a characteristic property of the WZNW model that it admits a higher spin linear realization of the extended affine Kac-Moody algebra which is equivalent to the corresponding higher spin nonlinear realization of the same algebra. However, in both cases, the higher spin Noether currents do not span an invariant space with respect to their generating transformations. Here, the current space is extended to an invariant space which allows us to gauge the symmetry.Supported by Bulgarian Foundation on Fundamental Research under contract Ph-318/93-95.     

Quantification of stable minor species in confined flames by cavity ring-down spectroscopy: application to NO

Cavity ring-down spectroscopy (CRDS) is used to measure the NO mole fraction formed in the burnt gases of low-pressure premixed flames. It is shown that the line-of-sight absorption is greatly increased by the contribution of the NO molecules surrounding the burner. This contribution has been quantified by developing a mathematical procedure taking into account the spatial and spectral features of the CRDS measurement. Calculations have been undertaken in the general case of a stable species not consumed in the flame. The most sensitive parameter is the temperature both in the flame and outside the flame. Simulations allow the selection of the best spectroscopic transitions for a given flame (i.e. a given temperature profile), ensuring the weakest influence of the inaccuracy affecting the temperature determination. High quantum states belonging to the A–X (0–1) band of NO have been found to be the most valuable and have led to a NO mole fraction determination with an accuracy of ±13%. NO absorption in the flame was completely masked using the A–X (0–0) band. Finally, the prompt-NO mole fraction formed in a methane/air flame stabilized at 33 Torr is obtained by combining CRDS and laser induced fluorescence techniques. Received: 12 October / Revised version: 1 February 2002 / Published online: 14 March 2002     

Orthonormal polynomial bases in function spaces

We construct polynomial orthonormal bases in various function spaces. Our bases have linear order of growth of degrees of polynomials. We show that this order is optimal.