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Factorization theorems, and properties of sets of eigenvectors, are established for regular selfadjoint quatratic matrix polynomials L(λ) whose leading coefficeint is indefinite or possibly singular, and for which all eigenvalues are real of definite type. The two linear factors obtained have spectra which are just the eigenvalues of L(λ) of positive and negative types, respectively. 相似文献
84.
Motivated by Bonahon’s result for hyperbolic surfaces, we construct an analogue of the Patterson–Sullivan–Bowen–Margulis map
from the Culler–Vogtmann outer space CV (F
k
) into the space of projectivized geodesic currents on a free group. We prove that this map is a continuous embedding and
thus obtain a new compactification of the outer space. We also prove that for every k ≥ 2 the minimum of the volume entropy of the universal covers of finite connected volume-one metric graphs with fundamental
group of rank k and without degree-one vertices is equal to (3k − 3) log 2 and that this minimum is realized by trivalent graphs with all edges of equal lengths, and only by such graphs.
Received: December 2005, Accepted: March 2006 相似文献
85.
High-resolution plane-wave decomposition in an auditorium using a dual-radius scanning spherical microphone array 总被引:1,自引:0,他引:1
The spatial and temporal distribution of early reflections in an auditorium is considered important for sound perception. Previous studies presented measurement and analysis methods based on spherical microphone arrays and plane-wave decomposition that could provide information on the direction and time of arrival of early reflections. This paper presents recent results of room acoustics analysis based on a spherical microphone array, which employs high spherical harmonics order for improved spatial resolution, and a dual-radius spherical measurement array to avoid ill-conditioning at the null frequencies of the spherical Bessel function. Spatial-temporal analysis is performed to produce directional impulse responses, while analysis based on the windowed Fourier transform is employed to detect direction of arrival of individual reflections at selected frequencies. Experimental results of sound-field analysis in a real auditorium are also presented. 相似文献
86.
Mikhail E. Minyaev Dmitrii M. Roitershtein Ilya E. Nifant'ev Ivan V. Ananyev Tatyana V. Minyaeva Timofey A. Mikhaylyev 《Acta Crystallographica. Section C, Structural Chemistry》2015,71(6):491-498
(1RS,2SR,3RS,4SR,5RS)‐2,4‐Dibenzoyl‐1,3,5‐triphenylcyclohexan‐1‐ol or (4‐hydroxy‐2,4,6‐triphenylcyclohexane‐1,3‐diyl)bis(phenylmethanone), C38H32O3, (1), is formed as a by‐product in the NaOH‐catalyzed synthesis of 1,3,5‐triphenylpentane‐1,5‐dione from acetophenone and benzaldehyde. Single crystals of the chloroform hemisolvate, C38H32O3·0.5CHCl3, were grown from chloroform. The structure has triclinic (P) symmetry. One diastereomer [as a pair of (1RS,2SR,3RS,4SR,5RS)‐enantiomers] of (1) has been found in the crystal structure and confirmed by NMR studies. The dichoromethane hemisolvate has been reported previously [Zhang et al. (2007). Acta Cryst. E 63 , o4652]. (1RS,2SR,3RS,4SR,5RS)‐2,4‐Dibenzoyl‐3,5‐bis(2‐methoxyphenyl)‐1‐phenylcyclohexan‐1‐ol or [4‐hydroxy‐2,6‐bis(2‐methoxyphenyl)‐4‐phenylcyclohexane‐1,3‐diyl]bis(phenylmethanone), C40H36O5, (2), is also formed as a by‐product, under the same conditions, from acetophenone and 2‐methoxybenzaldehyde. Crystals of (2) have been grown from chloroform. The structure has orthorhombic (Pca21) symmetry. A diastereomer of (2) possesses the same configuration as (1). In both structures, the cyclohexane ring adopts a chair conformation with all bulky groups (benzoyl, phenyl and 2‐methoxyphenyl) in equatorial positions. The molecules of (1) and (2) both display one intramolecular O—H...O hydrogen bond. 相似文献
87.
Artur Vashurin Vladimir Maizlish Ilya Kuzmin Oleg Petrov Mikhail Razumov Svetlana Pukhovskaya Oleg Golubchikov Oscar Koifman 《Journal of inclusion phenomena and macrocyclic chemistry》2017,87(1-2):37-43
The influence of the size of conjugated π-system on catalytic activity of cobalt complex with β-octaphenylporphyrin and its tetraaza-, tetrabenzo and tetrabenzotetraaza derivatives was studied in present work. It is found that catalytic activity for oxidation of sulfur-containing compounds increases under extension of conjugated macrocycle system according to the following series CoP < CoBP ≤ CoPz < CoPPz ? CoPc. 相似文献
88.
On a single discrete scale for preventive maintenance with two shock processes affecting a complex system
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A new approach to optimal maintenance of systems (networks) is suggested. It is applied to systems subject to two external independent shock processes. A system ‘consists’ of two parts, and each shock process affects only its own part. A new notion of bivariate signature is suggested and used for obtaining survival characteristics of a system and further optimization of the preventive maintenance actions. The preventive maintenance optimization is considered in the univariate discrete scale that counts the overall numbers of shocks of both types. An example of a transportation network is considered. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
89.
90.
Gurinov AA Rozhkova YA Zukal A Čejka J Shenderovich IG 《Langmuir : the ACS journal of surfaces and colloids》2011,27(19):12115-12123
(1)H and variable-temperature (15)N NMR techniques have been used to study the effect of the gradual alumination of SBA-15 on the structure and adsorption properties of this mesoporous material. The interpretation of experimental spectra suggests that aluminum chlorhydrol most effectively reacts with silica surfaces in the confinement of the cavities of rough mesopore walls, instead of forming a homogeneous aluminum film. This first leads to a gradual filling of the cavities and finally results in aluminum islands on the inner surfaces of mesopores. In the sample with a Si/Al atomic ratio of 4.1, up to half of the inner surface area of the mesopores is covered with aluminum. The alumination produces Br?nsted acid sites attributed to silanol groups interacting with aluminum but does not affect the proton-donating ability of isolated silanol groups. At high Si/Al ratios, the surface contains only one type of Lewis site attributed to tetracoordinated aluminum. At lower Si/Al ratios, Lewis acid sites with a lower electron-accepting ability appear, as attributed to pentacoordinated aluminum. The numerical values of the surface densities of all chemically active sites have been estimated after annealing at 420 and 700 K. We were surprised to observe that gaseous nitrogen can occupy Lewis acid sites and hinder the interaction of the aluminum with any other electron donor. As a result, aluminated surfaces saturated with nitrogen do not exhibit any Br?nsted or Lewis acidity. At room temperature, it takes days before pyridine replaces nitrogen at the Lewis acid sites. 相似文献