Linear Independence of q-Analogues of Certain Classical Constants

Let K be ? or an imaginary quadratic number field, and q ∈ K an integer with ¦q¦ > 1. We give a quantitative version of Σ_n≥1 a_n/(qⁿ ? 1) ? K for non-zero periodic sequences (a_n) 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     

Electronic properties of model quantum-dot structures in zero and finite magnetic fields

We have computed electronic structures and total energies of circularly confined two-dimensional quantum dots and their lateral dimers in zero and finite uniform external magnetic fields using different theoretical schemes: the spin-density-functional theory (SDFT), the current-and-spin-density-functional theory (CSDFT), and the variational quantum Monte Carlo (VMC) method. The SDFT and CSDFT calculations employ a recently-developed, symmetry-unrestricted real-space algorithm allowing solutions which break the spin symmetry. Results obtained for a six-electron dot in the weak confinement limit and in zero magnetic field as well as in a moderate confinement and in finite magnetic fields enable us to draw conclusions about the reliability of the more approximative SDFT and CSDFT schemes in comparison with the VMC method. The same is true for results obtained for the two-electron quantum dot dimer as a function of inter-dot distance. The structure and role of the symmetry-breaking solutions appearing in the SDFT and CSDFT calculations for the above systems are discussed. Received 16 October 2001 and Received in final form 17 January 2002     

Reflection of Long Game Formulas

We study game formulas the truth of which is determined by a semantical game of uncountable length. The main theme is the study of principles stating reflection of these formulas in various admissible sets. This investigation leads to two weak forms of strict-II¹₁ reflection (or ∑₁-compactness). We show that admissible sets such as H(ω₂) and L_ω2 which fail to have strict-II¹₁ reflection, may or may not, depending on set-theoretic hypotheses satisfy one or both of these weaker forms. Mathematics Subject Classification : 03C70, 03C75.     

Rotational bands in 181Ta

High-spin states in ¹⁸¹Ta have been studied via the ¹⁷⁶Yb(¹¹B,α2n) reaction at 52 MeV using the PEX array and at 57 MeV using the NORDBALL array, with α-particle detection. The previously known, K^π=(7/2)⁺ ground state band and K^π=(9/2)⁻ band have been extended to spins (29/2)⁺ and (31/2)⁻, respectively. Two new one-quasiparticle bands, the K^π=(5/2)⁺ band built on the known (5/2)⁺ isomer and a K^π=((1/2)⁻) band have been observed. Two other rotational bands with three-quasiparticle structure, K^π=(15/2)⁻ and ((19/2)⁺ with π(7/2)[404]ν²(1/2)[510](9/2)[624] and π(9/2)[514]ν²(1/2)[510](9/2)[624] configurations, respectively, have been newly observed. The half-life of the K^π=((19/2)⁺) bandhead which decays to the head of the (15/2)⁻ band has been measured to be 140(36) ns. However, transitions from the ((19/2)⁺) state to the (15/2)⁻ band have not been observed. Received: 26 August 1998     

Thermal and spectroscopic investigation of europium and samarium sulphates hydrates by TG-FTIR and ICP-MS techniques

The investigation of europium(III) sulphate hydrate and samarium(III) sulphate hydrate was performed by thermal analysis (TG-DTG) and simultaneous infrared evolved gas analysis-Fourier transformed infrared (EGA-FTIR) spectroscopy. The TG, DTG and DTA curves were recorded at the 25–1400 °C in the dynamic air atmosphere by TG/DTA analyser. The infrared evolved gas analysis was obtained on the FTIR spectrometer. Eu₂(SO₄)₃·nH₂O (n = 3.97) and Sm₂(SO₄)₃·nH₂O (n = 8.11) were analysed, the dehydration and decomposition steps were investigated and the water content was calculated. The formation of different oxysulphates was studied.

The trace rare earth elements in Eu and Sm sulphates were determined by ICP-MS. The concentration of trace Eu, Sm, La, Gd, Y and Ce ranged from 3.9 × 10⁻⁶ to 1.5 × 10⁻⁴% (m/m).     

Organo-noble-gas hydride compounds HKrCCH, HXeCCH, HXeCC, and HXeCCXeH: formation mechanisms and effect of 13C isotope substitution on the vibrational properties

We investigate the formation mechanism of HXeCCXeH in a Xe matrix. Our experimental results show that the HXeCCXeH molecules are formed in the secondary reactions involving HXeCC radicals. The experimental data on the formation of HXeCCXeH is fully explained based on the model involving the HXeCC+Xe+H-->HXeCCXeH reaction. This reaction is the first case when a noble-gas hydride molecule is formed from another noble-gas molecule. In addition, we investigate the (12)C/(13)C isotope effect on the vibrational properties of organo-noble-gas hydrides (HKrCCH, HXeCCH, HXeCC, and HXeCCXeH) in noble-gas matrixes. The present experimental results and ab initio calculations on carbon isotope shifts of the vibrational modes support the previous assignments of these molecules. Upon (12)C to (13)C isotope substitution, we observed a pronounced effect on the H-Kr stretching mode of HKrCCH (downshift of 1.0-3.6 cm(-1), depending on the matrix site) and a small anomalous shift (+0.1 cm(-1)) of the H-Xe stretching mode of HXeCCH and HXeCCXeH.     

Geometry prediction of hafnocenes by quantum chemical methods

The performance of quantum chemical methods for geometry prediction of hafnocenes was evaluated. HF, B3LYP and MP2 in combination with nonrelativistic (MHF) and relativistic (MWB and LANL2DZ) basis sets for hafnium together with standard basis sets 3-21G*, 6-31G* and 6-311G** for other elements were applied. Five basic structural parameters of the optimized structures of the hafnocenes were compared with experimental crystal structures obtained from the Cambridge structural database. Altogether 80 hafnocenes were included in the analysis. The results show that relativistic corrections are necessary for Hf atom. However, even the Hartree–Fock (HF) method, when combined with relativistic pseudopotentials, reproduces the experimental crystal structures with significant accuracy. The good performance of the HF method can be understood to originate from the absence of significant near-degeneracy correlations for hafnium. On average, the B3LYP and MP2 methods provide structural parameters somewhat closer to the experimental ones.     

IR-induced processes for allyl alcohol dimers involving an intermolecular OH...π Bond in low-temperature matrices

Sharp peaks were observed in the IR spectra of allyl alcohol dimers in the νOH and τOH regions in low-temperature Ar and N₂ matrices. In Ar a peak at 3587 cm^?1 was found to increase in intensity upon annealing and decrease upon IR irradiation; it is concluded that this peak is due to an OH...π interaction (of a cyclic structure) present in part of the dimers. This is the first time such an interaction and photoprocess have been found for an alcohol in matrices. Also a faster photo-process was found. Confomer changes in the monomers accompany the photoprocess in allyl alcohol dimers.     

Additivity of inelastic gamma ray scattering in methanol—water and ethanol—water solutions

Compton profiles of water, methanol, ethanol and mixtures of methanol—water and ethanol—water have been measured using 60 keV gamma rays from a 5 Ci annular²⁴¹ Am source. The profile of each mixture has been compared with the profile of the sum of the components and at all concentrations a linear behaviour has been found.