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41.
A. I. Shtern 《Russian Journal of Mathematical Physics》2006,13(2):210-223
As was proved by van der Waerden in 1933, every finite-dimensional locally bounded representation of a semisimple compact
Lie group is continuous. This is the famous “van der Waerden continuity theorem,” and it motivated a vast literature. In particular,
relationships between the assertion of the theorem (and of the inverse, in a sense, to this theorem) and some properties of
the Bohr compactifications of topological groups were established, which led to the introduction and the study of certain
classes of the so-called van der Waerden groups and algebras. Until now, after more than 70 years have passed, the van der
Waerden theorem appears in monographs and surveys in diverse forms; new proofs were found and then simplified in important
special cases.
In this paper, we prove that the statement of the van der Waerden theorem remains valid for all (not necessarily compact)
real semisimple Lie groups, i.e., any given finite-dimensional representation of a real semisimple Lie group is continuous
if and only if this representation is locally bounded.
More subtle results are also obtained. The main theorem contains several conditions equivalent to the continuity condition
for a finite-dimensional representation. In particular, it is proved that every finite-dimensional representation of a real
semisimple Lie group is continuous if and only if the restriction of this representation to the “compact” part, to the Abelian
part, or to the nilpotent part of the Iwasawa decomposition is locally bounded, and the original van der Waerden theorem is
also somewhat refined. For instance, the following assertion holds: every finite-dimensional representation of a compact semisimple
Lie group is continuous if and only if the restriction of this representation to some maximal torus is locally bounded.
Dedicated to the memory of George Mackey (1916–2006)
Partially supported by the Russian Foundation for Basic Research under grant no. 02-01-00574, by the Program of Supporting
the Leading Scientific Schools under grant no. NSh 619.203.1, and by the INTAS grant. 相似文献
42.
A. I. Nazarov 《Journal of Mathematical Sciences》2006,133(3):1314-1327
We find logarithmic small ball asymptotics for the L2-norm with respect to self-similar measures for a certain class of Gaussian processes including Brownian motion, Ornstein-Uhlenbeck
process, and their integrated counterparts. Bibliography: 46 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 311, 2004, pp. 190–213. 相似文献
43.
Using the method of the tensor Green’s function of the wave equation, the differential and total cross sections for the scattering of surface optical electromagnetic waves (surface plasmon polaritons) by a spherical nanoparticle into surface plasmon polaritons and light have been obtained with the inclusion of the magnetic dipole contribution. Using the example of noble metal systems, it has been shown that the magnetic dipole contribution may significantly affect the angular dependence of the differential cross sections and increase their anisotropy as the plasmon wavelength increases. 相似文献
44.
J. Maul I. Strachnov S. Karpuk P. Bernhard A. Oelsner G. Schönhense G. Huber 《Applied Physics A: Materials Science & Processing》2006,82(1):43-47
We report morphologic changes of metallic surfaces at the onset of ablation, starting from gentle ablation to the emergence of ablation craters. The evolution of both observed melting zones and of ablation craters therein are investigated in dependence of the ablation laser fluence for nanosecond ultraviolet laser pulses. Further, consequences of crater formation for cluster synthesis within the released atomic vapor are pointed out. PACS 52.38.Mf; 79.20.Ds; 65.40.De 相似文献
45.
Space-time directional Lyapunov exponents are introduced. They describe the maximal velocity of propagation to the right or to the left of fronts of perturbations in a frame moving with a given velocity. The continuity of these exponents as function of the velocity and an inequality relating them to the directional entropy is proved. 相似文献
46.
Zoltá n M. Balogh Marianna Csö rnyei 《Proceedings of the American Mathematical Society》2006,134(9):2667-2675
We give sufficient conditions for Sobolev and Lipschitz functions in terms of their lower scaled-oscillation. The sharpness of these conditions is shown by examples. Our examples also show that a Stepanov-type differentiability theorem does not hold under the boundedness assumption of the lower scaled-oscillation.
47.
48.
M. V. Kartikeyan G. Singh E. Borie B. Piosczyk M. Thumm 《International Journal of Infrared and Millimeter Waves》2006,27(5):657-670
The feasibility of an 84 GHz, 500 kW, CW gyrotron for ECRH on an experimental tokamak will be presented in this paper. Mode
competition and mode selection procedures are carefully investigated by considering various candidate modes and the TE10,4 mode is chosen as the operating mode. A conventional cylindrical cavity resonator with weak input and output tapers and parabolic
roundings is considered for interaction studies. Self-consistent, both single mode and time-dependent, calculations are carried
out and power and efficiencies are computed for a typical set of beam parameters. The results show that an output power of
well over 500 kW, CW and efficiency around 40% can be reached without a depressed collector. 相似文献
49.
I. N. Sergeev 《Journal of Mathematical Sciences》2006,135(1):2764-2793
The definition of the characteristic frequencies of zeroes and changes of sign for solutions is given. It is equal to the
upper medium (with respect to the time half-axis) of their number on the half-interval of length π. We also define the main frequencies for a linear homogeneous equation of order n. These main frequencies for an equation with constant coefficients coincide with the absolute values of the imaginary parts
of the roots of the corresponding characteristic polynomial. It is proved that for the second-order equation the main frequencies
are the same for all solutions and that they are stable with respect to uniformly small and infinitely small perturbations
of the coefficients. For the third-order equation they can be different, and for any of the main frequencies an example of
nonstability is given.
__________
Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 25, pp. 249–294, 2005. 相似文献
50.
In this paper, a two-dimensional finite volume unstructured mesh method (FVUM) based on a triangular background interpolation mesh is developed for analysing the evolution of the saltwater intrusion into single and multiple coastal aquifer systems. The model formulation consists of a ground-water flow equation and a salt transport equation. These coupled and non-linear partial differential equations are transformed by FVUM into a system of differential/algebraic equations, which is solved using backward differentiation formulas of order one through five. Simulation results are compared with previously published solutions where good agreement is observed. 相似文献