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111.
112.
Let F
k
be a free group of rank k ≥ 2 with a fixed set of free generators. We associate to any homomorphism φ from F
k
to a group G with a left-invariant semi-norm a generic stretching factor, λ(φ), which is a noncommutative generalization of the translation number. We concentrate on the situation where φ: F
k
→ Aut(X) corresponds to a free action of F
k
on a simplicial tree X, in particular, where φ corresponds to the action of F
k
on its Cayley graph via an automorphism of F
k
. In this case we are able to obtain some detailed “arithmetic” information about the possible values of λ = λ(φ). We show that λ ≥ 1 and is a rational number with 2kλ ∈ ℤ[1/(2k − 1)] for every φ ∈ Aut(F
k
). We also prove that the set of all λ(φ), where φ varies over Aut(F
k
), has a gap between 1 and 1+(2k−3)/(2k
2−k), and the value 1 is attained only for “trivial” reasons. Furthermore, there is an algorithm which, when given φ, calculates λ(φ).
The second and the third author were supported by the NSF grant DMS#0404991 and the NSA grant DMA#H98230-04-1-0115. 相似文献
113.
The three-level system subjected to electromagnetic fields is investigated. It is shown that when one of two fields is strong (the pumping field), the system can amplify the second (probe) field even if no population inversion is created, but some phase relations are satisfied. The conditions necessary for inversionless amplification to take place are discussed. The connection between this effect and stimulated Raman emission is shown. Numerical simulations for each one of the discussed cases were performed. 相似文献
114.
Gaspar Ana B. Ksenofontov Vadim Spiering Hartmut Reiman Sergey Real José A. Gütlich Philipp 《Hyperfine Interactions》2002,144(1-4):297-306
This article reports on the study of the interplay between magnetic coupling and spin transition in 2,2′-bipyrimidine (bpym)-bridged
iron(II) dinuclear compounds. Coexistence of both phenomena has been observed in [Fe(bpym)(NCS)2]2bpym, [Fe(bpym)(NCSe)2]2bpym and [Fe(bt)(NCS)2]2bpym (bpym = 2,2′-bipyrimidine, bt = 2,2′-bithiazoline) by the action of external physical factors namely pressure or electromagnetic
radiation. Competition between magnetic exchange and spin crossover has been studied in [Fe(bpym)(NCS)2]2bpym at 6.3 kbar. LIESST experiments carried out in [Fe(bpym)(NCSe)2]2bpym and [Fe(bt)(NCS)2]2bpym at 4.2 K have shown that is possible to achieve dinuclear molecules with different spin states in this class of compounds.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
115.
116.
We derive necessary and sufficient conditions for a one-dimensional periodic Schrödinger (i.e., Hill) operator in to be a spectral operator of scalar type. The conditions demonstrate the remarkable fact that the property of a Hill operator being a spectral operator is independent of smoothness (or even analyticity) properties of the potential V. To cite this article: F. Gesztesy, V. Tkachenko, C. R. Acad. Sci. Paris, Ser. I 343 (2006). 相似文献
117.
118.
An experimental, temperature-dependent kinetic study of the gas-phase reaction of the hydroxyl radical with molecular bromine (reaction 1) has been performed by using a pulsed laser photolysis/pulsed-laser-induced fluorescence technique over a wide temperature range of 297-766 K, and at pressures between 6.68 and 40.29 kPa of helium. The experimental rate coefficients for reaction 1 demonstrate no correlation with pressure and exhibit a negative temperature dependence with a slight negative curvature in the Arrhenius plot. A nonlinear least-squares fit with two floating parameters of the temperature-dependent k(1)(T) data set using an equation of the form k(1)(T) = AT(n) yields the recommended expression k(1)(T) = (1.85 x 10(-9))T(-0.66) cm(3) molecule(-1) s(-1) for the temperature dependence of the reaction 1 rate coefficient. The potential energy surface (PES) of reaction 1 was investigated with use of quantum chemistry methods. The reaction proceeds through formation of a weakly bound OH...Br(2) complex and a PES saddle point with an energy below that of the reactants. Temperature dependence of the reaction rate coefficient was modeled by using the RRKM method on the basis of the calculated PES. 相似文献
119.
Annenkov VV Patwardhan SV Belton D Danilovtseva EN Perry CC 《Chemical communications (Cambridge, England)》2006,(14):1521-1523
A new method for the stepwise synthesis of propylamines containing fragments of N-methyl propylamine as found in diatom bioextracts is presented and their activity in silicic acid condensation is described. 相似文献
120.