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101.
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
102.
The paper deals with finite–difference (f-d) approach to simulation of elastic waves' propagation in anisotropic elastic media with general symmetry. Any implementation of this approach claims resolution of two key problems:
- construction of an effective f-d scheme itself; we propose to use the Lebedev's scheme (LS) being a natural generalization of Virieux staggered grid scheme (VS) widely used for isotropy; we prove that LS possesses better dispersion properties in comparison with well known Rotated Staggered Grids Scheme (RSGS).
- stable domain distension. The Perfectly Matched Layers(PML) useful for isotropic problems can be unstable in the case of anisotropy. Lebedev scheme allows one to use Optimal Grids (OG) which gives a possibility to implement efficient and low cost domain distension.
103.
Vadim Mogilevskii 《Journal of Functional Analysis》2011,261(7):1955-1968
Let H be a Hilbert space and let A be a simple symmetric operator in H with equal deficiency indices d:=n±(A)<∞. We show that if, for all λ in an open interval I⊂R, the dimension of defect subspaces Nλ(A) (=Ker(A?−λ)) coincides with d, then every self-adjoint extension has no continuous spectrum in I and the point spectrum of is nowhere dense in I. Application of this statement to differential operators makes it possible to generalize the known results by Weidmann to the case of an ordinary differential expression with both singular endpoints and arbitrary equal deficiency indices of the minimal operator. 相似文献
104.
Journal of Algebraic Combinatorics - A set $$S\subseteq V$$ is independent in a graph $$G=\left( V,E\right) $$ if no two vertices from S are adjacent. The independence number $$\alpha (G)$$ is the... 相似文献
105.
Vadim Kaimanovich 《Israel Journal of Mathematics》1995,89(1-3):77-134
Covering Markov operators are a measure theoretical generalization of both random walks on groups and the Brownian motion
on covering manifolds. In this general setup we obtain several results on ergodic properties of their Poisson boundaries,
in particular, that the Poisson boundary is always infinite if the deck group is non-amenable, and that the deck group action
on the Poisson boundary is amenable. For corecurrent operators we show that the Radon-Nikodym cocycles of two quotients of
the Poisson boundary are cohomologous iff these quotients coincide. It implies that the Poisson boundary is either purely
non-atomic or trivial, and that the action of any normal subgroup of the deck group on the Poisson boundary is conservative.
We show that the Poisson boundary is trivial for any corecurrent covering operator with a nilpotent (or, more generally, hypercentral)
deck group. Other applications and examples are discussed.
Supported by a British SERC Advanced Fellowship. A part of this work was done during my stay at MSRI, Berkeley supported by
NSF Grant DMS 8505550. 相似文献
106.
107.
Mikhail Y. Shalaginov Vadim V. Vorobyov Jing Liu Marcello Ferrera Alexey V. Akimov Alexei Lagutchev Andrey N. Smolyaninov Vasily V. Klimov Joseph Irudayaraj Alexander V. Kildishev Alexandra Boltasseva Vladimir M. Shalaev 《Laser \u0026amp; Photonics Reviews》2015,9(1):120-127
The broadband enhancement of single‑photon emission from nitrogen‐vacancy centers in nanodiamonds coupled to a planar multilayer metamaterial with hyperbolic dispersion is studied experimentally. The metamaterial is fabricated as an epitaxial metal/dielectric superlattice consisting of CMOS‐compatible ceramics: titanium nitride (TiN) and aluminum scandium nitride (AlxSc1‐xN). It is demonstrated that employing the metamaterial results in significant enhancement of collected single‑photon emission and reduction of the excited‐state lifetime. Our results could have an impact on future CMOS‐compatible integrated quantum sources.
108.
109.
Kessler VG 《Chemical communications (Cambridge, England)》2003,(11):1213-1222
General principles of formation and stability of the heterometallic alkoxides existing due to Lewis Acid-Base interaction, isomorphous substitution and heterometallic metal-metal bonds are discussed. The molecular structure design approach based on the choice of a proper molecular structure type and completing it with the ligands, providing both the necessary number of donor atoms and the sterical protection of the metaloxygen core, is presented. Its applications in prediction of the composition and structure of single source precursors of inorganic materials are demonstrated for such classes of compounds as oxoalkoxides, alkoxide beta-diketonates, alkoxide carboxylates, derivatives of functional alcohols, metallatranes and metallasiloxanes. 相似文献
110.
Gradinaru J Forni A Druta V Tessore F Zecchin S Quici S Garbalau N 《Inorganic chemistry》2007,46(3):884-895
New unsymmetrical [N2O2] tetradentate Schiff base complexes of Ni(II), Cu(II), Zn(II), and VO(II) were synthesized by template condensation of the tetradentate precursor 1-phenylbutane-1,3-dione mono-S-methylisothiosemicarbazone with o-hydroxybenzaldehyde or its 5-phenylazo derivative. They were characterized by elemental analysis, IR, UV-vis, electron spin resonance, and NMR spectroscopy, mass spectrometry, and magnetic measurements. The crystal structures of five of them have been determined by X-ray diffraction using, in some cases, synchrotron radiation. These compounds are characterized by a large thermal stability; their decomposition temperatures range from 240 up to 310 degrees C. Complexes with the phenylazo substituent were found to possess a large second-order nonlinear optical (NLO) response, as determined both by measurements of solution-phase direct current electric-field-induced second harmonic generation and by theoretical time-dependent density functional theory (TDDFT) calculations. The molecular hyperpolarizability was found to decrease in the order Zn(II) > Cu(II) > Ni(II) approximately VO(II). The active role of the metal in determining the NLO properties of the complexes was shown through an analysis of their UV-vis spectra, which revealed the presence of metal-to-ligand (in closed-shell complexes) and ligand-to-metal (in open-shell complexes) charge-transfer bands together with intra-ligand charge-transfer transitions. Assignment of the bands was based on the analysis of the TDDFT computed spectra. 相似文献