Periodic Integrable Systems with Delta-Potentials

In this paper we study root system generalizations of the quantum Bose-gas on the circle with pair-wise delta-function interactions. The underlying symmetry structures are shown to be governed by the associated graded algebra of Cherednik's (suitably filtered) degenerate double affine Hecke algebra, acting by Dunkl-type differential-reflection operators. We use Gutkin's generalization of the equivalence between the impenetrable Bose-gas and the free Fermi-gas to derive the Bethe ansatz equations and the Bethe ansatz eigenfunctions.     

Chaos and hyperchaos in a gyrotron

We study oscillation in a gyrotron with allowance for reflections from an output horn. Regions with different system behaviors, such as stationary oscillation, self-modulation, and complex-dynamics regimes are found in the parameter plane. The scenarios of appearance of chaotic oscillations are considered. It is shown that they can emerge via either a sequence of period-doubling bifurcations or destruction of quasiperiodic motion. For chaotic attractors, Lyapunov exponents are calculated and their dimensions are estimated on the basis of the Kaplan-Yorke formula. The dimension values turn out to be anomalously large, which is stipulated by the presence of a large number of high-Q eigenmodes in the gyrotron cavity due to operation near the cutoff frequency of an electrodynamic system. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 10, pp. 887–899, October 2006.     

Application of rainbow schlieren deflectometry to measure temperature and oxygen concentration in a laminar gas-jet diffusion flame

The quantitative rainbow schlieren deflectometry (RSD) technique was applied to measure temperature and oxygen concentration in an axisymmetric hydrogen gas-jet diffusion flame burning in quiescent air at fuel jet exit Reynolds number of 70. Schlieren measurements were compared with conventional measurements using a thermocouple and a gas-sampling probe. Good agreement between the two measurement techniques was achieved on the fuel-lean side of the flame.     

Coxeter Transformation and Quasiquivers

Mathematical Notes -     

On f-injective modules

In this paper, the notions of f-injective and f^*-injective modules are introduced. Elementary properties of these modules are given. For instance, a ring R is coherent iff any ultraproduct of f-injective modules is absolutely pure. We prove that the class S^* \Sigma^* of f^*-injective modules is closed under ultraproducts. On the other hand, S^* \Sigma^* is not axiomatisable. For coherent rings R, S^* \Sigma^* is axiomatisable iff every c₀ \chi_0 -injective module is f^*-injective. Further, it is shown that the class S \Sigma of f-injective modules is axiomatisable iff R is coherent and every c₀ \chi_0 -injective module is f-injective. Finally, an f-injective module H, such that every module embeds in an ultraprower of H, is given.     

Unconditional Bases, the Matrix Muckenhoupt Condition, and Carleson Series in a Spectrum

Two families of functions constructed by a system of n scalar Muckenhoupt weights are studied. Criteria are given under which these families are unconditional bases. From the point of view of the spectral operator theory, the problem is reduced to the study of the structure of n-dimensional perturbations of the integration operator. Weighted estimates for the Hilbert transform in the spaces of vector-functions are applied to construct an operator mapping functions of the studied families to vector-valued rational functions. The concept of the Carleson series is used in the study of the following problem: when do vector-valued rational functions form an unconditional basis? Bibliography: 8 titles.     

Numerical solutions of the shallow water equations with discontinuous bed topography

A simple scheme is developed for treatment of vertical bed topography in shallow water flows. The effect of the vertical step on flows is modelled with the shallow water equations including local energy loss terms. The bed elevation is denoted with z_b^‐ for the left and z_b⁺ for the right values at each grid point, hence exactly representing a discontinuity in the bed topography. The surface gradient method (SGM) is generalized to reconstruct water depths at cell interfaces involving a vertical step so that the fluxes at the cell interfaces can accurately be calculated with a Riemann solver. The scheme is verified by predicting a surge crossing a step, a tidal flow over a step and dam‐break flows on wet/dry beds. The results have shown good agreements compared with analytical solutions and available experimental data. The scheme is efficient, robust, and may be used for practical flow calculations. Copyright © 2002 John Wiley & Sons, Ltd.     

Cytotoxic acetylenes from Panax quinquefolium

Three new cytotoxic polyacetylenes, PQ-1 (1), PQ-2 (2) and PQ-3 (3), have been isolated from Panax quinquefolium. The structures of these acetylenes were determined by analyses of their 1H-1H and 1H-13C COSY spectra. All these compounds exhibited strong cytotoxic activities against leukemia cells (L 1210) in tissue culture.     

Effect of trapping centers of luminescent properties of bismuth orthogermanate

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 54, No. 6, pp. 970–975, June, 1991.     

Higher-dimensional homogeneous cosmological models as autonomous dynamical systems

The field equations for homogeneous models in an arbitrary number of dimensions form a Hamiltonian system with constraint forces. Due to the monotonic behavior of the determinant of the induced metric, the evolution of the system can be interpreted as the motion of a particle in an explicitly time-dependent potential. Considering vacuum models, we show that this explicit time-dependence can be eliminated. Using the scaling properties of the Ricci tensor we obtain an autonomous system, for which we can also find a Liapunov function in terms of the n-dimensional Ricci curvature.