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121.
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. 相似文献
122.
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. 相似文献
123.
V. I. Dashkevich 《Journal of Applied Spectroscopy》2002,69(6):862-870
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. 相似文献
124.
125.
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. 相似文献
126.
Necessary conditions for the Gâteaux differentiability of the distance function to a set are considered. A series of characterizing results is obtained. 相似文献
127.
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 相似文献
128.
Mathematical Notes - 相似文献
129.
130.
A. R. Volkov B. V. Shul'gin T. I. Polupanova V. N. Lebedev A. A. Nagornyi V. L. Petrov Yu. F. Kargin 《Journal of Applied Spectroscopy》1991,54(6):585-590
Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 54, No. 6, pp. 970–975, June, 1991. 相似文献