Effect of the Parameters of Three-Mirror Resonators on the Spectral Characteristics of Single-Pulse Laser Generation with Self-Injection of Priming Radiation

Based on a semiclassical theory, investigations were made of the dynamics and spectral composition of pulsed generation with self-injection of priming radiation from the active part of a three-mirror linear resonator, the passive part of which contains an active loss modulator and serves as the output reflector of the laser. It is shown that there exists a range of resonator parameters at which pulsed lasing has virtually a single frequency irrespective of the detuning of the frequencies of the priming radiation and of the nearest eigenmode of the composite resonator. Considering graphically the phase conditions of generation, it is established that among pulsed lasers with self-injection of priming radiation which are constructed on the basis of three-mirror linear and branched resonators, the most efficient for creating single-frequency generation are those in which the length of the main resonator, where generation of the pulse occurs, is larger than the length of the additional one intended for forming the priming radiation. With an inverse ratio of the lengths of the resonators, the conditions of single-frequency pulsed generation becomes dependent on the priming radiation frequency.     

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.     

Velocity measurements in liquid sodium by means of ultrasound Doppler velocimetry

A successful application of ultrasound Doppler velocimetry in liquid sodium flows is described. To obtain sufficient Doppler signals, different problems had to be solved: the transmission of the ultrasonic beam through the channel wall made of stainless steel, the acoustic coupling between the transducer and the channel wall, and the wetting of the inner surface of the wall by the liquid metal, respectively. A sodium flow in a square duct exposed to a transverse magnetic field is investigated. In accordance with the existing knowledge about MHD channel flows, we found that the velocity profiles modified to a M-shape owing to the effect of an inhomogeneous magnetic field. Received: 12 June 2001/Accepted: 27 October 2001     

Parametric resonance in the problem of a heavy rigid body rolling along a straight line on a plane

The problem of the stability of a heavy rigid body, bounded by the surface of an ellipsoid and with a cavity in the form of a coaxial ellipsoid, rolling along a straight line on a horizontal rough plane is investigated. It is shown that in the case of a body that is close to being dynamically symmetrical, parametric resonance always occurs leading to instability of the rolling. Each ellipsoid has its own “individual” resonance angular velocity. In the general case, regions in which the necessary stability conditions are satisfied can be distinguished in parameter space. The problem of calculating the resonance coefficient corresponding to instability for parametric resonance in a reversible third-order system is solved.     

Necessary Conditions for Differentiability of Distance Functions

Necessary conditions for the Gâteaux differentiability of the distance function to a set are considered. A series of characterizing results is obtained.     

Inclusion of carbon nanotubes in a TiO2 sol-gel matrix

We report here the successful inclusion of carbon nanotubes (CNs) into a TiO₂ matrix prepared by a sol-gel method. The presence of CNs in the sol-gel matrix and the structure of the film were analyzed principally by transmission electron microscopy. Complementary information about the behavior of embedded carbon nanotubes versus heat treatment and ion irradiation were obtained by X-ray photoelectron spectroscopy. The elaboration of an inorganic matrix containing embedded carbon nanotubes leads to a new nanocomposite. The possible applications of this nanocomposite are discussed.     

A nilpotent Roth theorem

Let T and S be invertible measure preserving transformations of a probability measure space (X, ℬ, μ). We prove that if the group generated by T and S is nilpotent, then exists in L ²-norm for any u, v∈L ^∞(X, ℬ, μ). We also show that for A∈ℬ with μ(A)>0 one has . By the way of contrast, we bring examples showing that if measure preserving transformations T, S generate a solvable group, then (i) the above limits do not have to exist; (ii) the double recurrence property fails, that is, for some A∈ℬ, μ(A)>0, one may have μ(A∩T _-n A∩S ^{- n} A)=0 for all n∈ℕ. Finally, we show that when T and S generate a nilpotent group of class ≤c, in L ²(X) for all u, v∈L ^∞(X) if and only if T×S is ergodic on X×X and the group generated by T ^-1 S, T ^-2 S ²,..., T ^-c S ^c acts ergodically on X. Oblatum 19-V-2000 & 5-VII-2001?Published online: 12 October 2001     

Coxeter Transformation and Quasiquivers

Mathematical Notes -