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961.
K. Y. Lin 《Journal of statistical physics》1987,49(1-2):269-279
The spontaneous magnetization of the Ising model on a 4–8 lattice with six different coupling constants and two different magnetic moments is studied. A formula for the spontaneous magnetization is proposed. The result agrees with the exact low-temperature series expansions up to the 12th order. 相似文献
962.
963.
964.
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
965.
Experimental and theoretical research into electric generators of singlet delta oxygen (SDO) for an oxygen-iodine laser made
at the Lebedev Physics Institute and TRINITI is discussed. Breakdown and current-voltage characteristics of self-sustained
electric discharge in SDO were studied both experimentally and theoretically, indicating that SDO and pure oxygen have quite
different electric features. The electric properties and spectroscopy of an e-beam sustained discharge (EBSD) in oxygen and oxygen gas mixtures were experimentally studied. A comprehensive numerical
model describing SDO kinetics in different kinds of discharge was developed. The pulsed EBSD in pure oxygen and its mixtures
with noble gases was shown to be very unstable and characterized by low input energy. When adding small amounts of carbon
monoxide or hydrogen, the electric stability of the EBSD increases, the specific input energy (SIE) per molecular component
being more than order of magnitude higher and coming to 6.5 kJ/(l atm(O2 + CO)) for the gas mixture O2: Ar: CO = 1: 1: 0.1. Theoretical calculations demonstrated that, for an SIE of 6.5 kJ/(l atm), the SDO yield may reach ∼20%,
exceeding its threshold value needed for oxygen-iodine laser operation at room temperature. The calibration of the optical
scheme for measuring the SDO absolute concentration and yield using the detection of luminescence of the SDO going from a
chemical SDO generator was performed. The measurement of the SDO yield demonstrated that it was ∼10.5% for an SIE of ∼3.0
kJ/(l atm(O2 + CO)), which is about 1.5 times less than the results of theoretical calculations for such an SIE. SDO production
in RF slab discharge ignited in oxygen gas mixtures was experimentally studied, experimental SDO yield being about 10%. The
choice of electrode material was demonstrated to be very important.
Original Text ? Astro, Ltd., 2006. 相似文献
966.
Alcindo A. Dos Santos Renan S. Ferrarini Jefferson L. Princival João V. Comasseto 《Tetrahedron letters》2006,47(50):8933-8935
A masked lithium homoenolate, generated by tellurium/lithium exchange, was reacted with epoxides. The lithium compound was also converted into other organometallics such as Grignard, and cuprates and the reactivity of those organometallics with epoxides was evaluated. The same building block was employed in the synthesis of (+/−)-frontalin. 相似文献
967.
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
968.
D. N. Zaporozhets 《Journal of Mathematical Sciences》2006,137(1):4525-4530
In this note, we find the distibution of the number of real zeros of a random polynomial. We also derive a formula for the
expected number of complex zeros lying in a given domain of the complex plane. Bibliography: 7 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 320, 2004, pp. 69–79. 相似文献
969.
The main result of the paper is a theorem, using which a new proof of Roth’s theorem is obtained, a new solvability criterion
for the matrix equation AX-YB = C is proved, a formula for a particular solution of the latter is derived, and the least of
the orders of square nonsingular matrices containing a given rectangular matrix as a submatrix is determined. Bibliography:
5 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 323, 2005, pp. 15–23. 相似文献
970.
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