Pointwise consistency of the hermite series density estimate

The Hermite series estimate of a density f?L_p, p > 1, convergessin the mean square to f (x) for almost all x? |R, ifN (n) → ∞ and N (n) / n² → ) as n → ∞, where N is the number of the Hermite functions in the estimate while n is the number of observations. Moreover, the mean square and weak consistency are equivalent. For m times differentiable densities, the mean squares convergence rate is O(n^?(2m?1)/2m). Results for complete convergence are also given.     

Fourier transform infrared investigations of phosphate-silicate coatings on iron

The influence of silica addition and of the annealing on the structure and properties of phosphate coatings are investigated. It has been observed that silica stabilizes phosphates and reduces the transport of iron towards the surface.     

Osmotic and activity coefficients of some pyridine complexes with halogenoacetic acids in benzene at 25°C

Osmotic coefficients measured by vapour pressure osmometry are reported for benzene solutions of complexes of pyridine with trifluoroacetic, dichloroacetic and chloroacetic acids at 25°C. Solute activities decrease with increasing concentration due to formation of self-associates. It is suggested that dipole-dipole interactions contribute substantially to the stability of the associates.     

Anti-Stokes Yb3+ emission--valuable structure information in spectra of rare earth compounds measured with FT-Raman spectrometers

Raman spectroscopy is a powerful and simple method which proved to be very useful in studies of solids. The most widely used Raman spectrometers are FT-Raman instruments with YAG:Nd(3+) laser as an excitation source. However, in the case of samples containing rare earth elements, the quality of FT-Raman spectra is often low due to strong fluorescence effects. We show that, in such cases, anti-Stokes part of the Raman spectra often contains strong, well resolved bands identified as multiphonon-assisted emission bands of Yb(3+) present as an impurity. We show on several examples that analysis of these bands may provide useful structure information, similar to that obtained by "Eu structure probe" method in optical spectroscopy. The Yb(3+) emission can be also measured using standard luminescence detection systems. However, the application of FT-Raman system allows one to obtain good quality spectra in a much cheaper, easier and faster way (in times as short as a few seconds). Moreover, high-sensitivity of FT-Raman spectrometers allows to detect even very small amounts of Yb(3+) impurity.     

Estimates of the energy of intramolecular hydrogen bonds

A method for the estimation of the energy of intramolecular hydrogen bonds in conjugated systems existing in a variety of conformations is presented. The method is applied to determine the intramolecular hydrogen bond energy in 3-aminopropenal and 3-aminopropenthial. According to the proposed estimation scheme, the intramolecular H-bond energies are found to be of the order of 5-7 kcal/mol. These results are compared with those obtained by using other estimation schemes as well as with the recent results by other authors. Also, the H-bond energies in dimers and trimers of the two molecules are calculated and compared with the corresponding data for internally hydrogen-bonded monomers. This comparison shows that the bond equalization effect is primarily due to proton donor-proton acceptor proximity. In comparison with intermolecular hydrogen bonds, the rigidity of the chelate skeleton enhances this proximity effect. The same effect can be seen in systems with intermolecular hydrogen bonds, although its magnitude is diminished because of the absence of additional forces which pull the proton donor and proton acceptor groups toward each other. No specific resonance-assisted origin of the intramolecular hydrogen bond energy seems to be needed to elucidate the energetics of these bonds.     

The emission spectrum of the CΣ–XΣ system of AlH

The ultraviolet spectrum of AlH has been investigated at high resolution between 42 000 and 45 000 cm⁻¹ using a conventional spectroscopic technique. The AlH molecules were formed and excited in an aluminium hollow-cathode lamp with two anodes, filled with a mixture of Ne carried gas and a trace of NH₃. The emission from the discharge was observed with a plane grating spectrograph and recorded by a photomultiplier tube. The 0–0, 1–1 and 1–2 bands of the C¹Σ⁺–X¹Σ⁺ transition have been identified and rotationally analyzed. The new data were elaborated with help of recent X¹Σ⁺ state parameters reported by White et al. [J. Chem. Phys. 99 (1993) 8371–8378] and by Szajna and Zachwieja [Eur. Phys. J. D. 55 (2009) 549–555]. Determined constants of the excited C¹Σ⁺ state include: T_e = 44 675.3711(57) cm⁻¹, ω_e = 1575.3357(42) cm⁻¹, ω_ex_e = [125.5] cm⁻¹, B_e = 6.66804(32) cm⁻¹, α_e = 0.55839(56) cm⁻¹, D_e = 2.23(13) × 10⁻⁴ cm⁻¹, β_e = 6.13(25) × 10⁻⁴ cm⁻¹ and r_e = 1.613132(39) Å. The C¹Σ⁺ state is found to be extensively perturbed in the v = 0 and 1 vibrational level at J = 20, 22 − 27 and J = 5 − 9, respectively. This was probably caused by the interaction with the vibrational levels of the outer minimum.     

Unified description of nonclassical uniaxial ferroelectric materials in order–disorder phase transitions

An equation of state accounting for coupling of the primary order parameter (here the polarization) with a secondary order parameter (here a strain ?) is used to describe the temperature dependences of the spontaneous polarization and of the electric susceptibility on external biasing field. A new scaling invariant and its explicit expression are given. The theory is exemplified by the effective critical behavior of the molecular ferroelectric crystals (CH₃NH₃)₅Bi₂Cl₁₁ (MAPCB) and (CH₃NH₃)₅Bi₂Br₁₁ (MAPBB).     

Coumarin synthesis on π-acidic surfaces

Catalysis with anion–π interactions is emerging as an important topic in supramolecular chemistry. Among the reactions explored so far on π-acidic surfaces, coumarin synthesis stands out as a cascade process with several coupled anionic transition states. Increasing π-acidity has been shown in a different context to increase transition-state stabilisation and thus catalytic activity. In this report, we explore the possible use of macrocycles to accelerate coumarin synthesis between two π-acidic surfaces. To our disappointment, we found that compared to monomeric π-acids, coumarin synthesis within divalent macrocycles is clearly slower. Hindered access to an overly confined active site within the macrocycles could possibly account for this loss in activity, but several other explanations are certainly possible. However, operational coumarin synthesis on monomeric π-acidic surfaces is shown to tolerate structural modifications. Best results are obtained with structures that aim for proximity without obstructing transition-state stabilisation on the π-acidic surface.