Let K be ? or an imaginary quadratic number field, and q ∈ K an integer with ¦q¦ > 1. We give a quantitative version of Σn≥1 an/(qn ? 1) ? K for non-zero periodic sequences (an) in K of period length ≤ 2. As a corollary, we get a quantitative version of the linear independence over K of 1, the q-harmonic series, and a q-analogue of log 2. A similar result on 1, the q-harmonic series, and a q-analogue of ζ(2) is also proved. Mathematics Subject Classification (2000): 11J72, 11J82 相似文献
The first stage in a multi-attribute value analysis is the development of a hierarchical structure of the attributes of the problem. This paper reports the process of developing such a structure for the problem of choosing a suitable mode of transport for radioactive waste. The initial hierarchy of attributes went through several stages of development as new insights emerged about the nature of the problem. Some of the reasons behind this restructuring are discussed, and several important questions about the structuring process are formulated. 相似文献
We develop a theory of the magnetic-zenith effect (MZE) observed upon the ionosphere modification by powerful radio waves.
The dependences of MZE on main parameters, such as the magnetic-field inclination angle, pump-wave frequency and power, and
angular width of HF beam are obtained. The optimal elevation angle of pump-wave beam is predicted.
__________
Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48, No. 9, pp. 772–787, September 2005. 相似文献
The influence of the substrate temperature Tsub (20–360°C) and the oxygen pressure P(O2) (5 × 10−3−0.13 Pa) in an evaporation chamber on the structure and phase composition of films prepared through laser sputtering of a vanadium target is investigated by electron diffraction and in situ transmission electron microscopy (with the use of the bend extinction contour technique for determining the bending of the crystal lattice). It is demonstrated that the oxygen content in the films increases with an increase in the oxygen pressure P(O2) at a fixed substrate temperature Tsub and decreases with an increase in the substrate temperature Tsub at a fixed oxygen pressure P(O2). The conditions responsible for the formation and composition of the crystalline (VO0.9) and amorphous (V2O3) phases in the films are determined. It is established that the phase composition of the film depends on the angle of condensation of the vapor-plasma flow. The crystallization of the V2O3 amorphous phase is accompanied by an increase in the density by 9.2%. It is revealed that the V2O3 spherulites growing in the amorphous film have a bent crystal lattice. The bending of the crystal lattice can be as large as ∼42 deg/μm.
Furocoumarins modified by amino acids were prepared by condensation of the N-hydroxysuccinimide ester of 3-(2,3,5-trimethyl-7-oxofuro[3,2-g]chromen-6-yl)propanoic acid with amino acids. 相似文献
Organometallic compounds Cp2TiCl2, (EtC5H4)2NbCl2, and (PriC5H4)2WCl2 were assessed as additives that control polymer chain growth in the polymerization of methyl methacrylate. In the presence of compounds mentioned in amounts comparable with that of the initiator, a uniform process with no gel-effect occured and respective linear increase in the molecular weight of the polymer up to high degrees of the monomer conversion was observed. 相似文献
The {1/2, 0, 1/2} nuclear superstructure in an La0.93Sr0.07MnO3 manganite orthorhombic crystal is revealed using thermal-neutron diffraction. It is demonstrated that this superlattice belongs to the class of distortion-type structures and is directly associated with a 1/16-type ordering of Mn4+ and Mn3+ ions in a collinear ferromagnetic phase of the La0.93Sr0.07MnO3 manganite. 相似文献