Interaction of humic and fulvic acids with nanoclusters of aluminum hydroxo cations on the surface of kaolinite according to IR spectroscopy data

We chemically modified the surface of kaolinite with nanoclusters of aluminum hydroxo cations. We have determined their composition and sizes. We have used IR spectroscopy to establish the interaction between the carbonyl and -diketone groups of fulvic and humic acids with the Lewis acid sites: coordination unsaturated Al³⁺ cations of the Al₁₃ nanoclusters. We have obtained spectral evidence for hydrogen bond formation between the carboxyl groups of fulvic acid and the hydroxyl groups of the aluminum hydroxo cations.__________Translated from Teoreticheskaya i Éksperimentalnaya Khimiya, Vol. 41, No. 1, pp. 45–49, January–February, 2005.     

A contribution to the measurement of the electron density of discharge plasma by means of a toroidal resonator

The paper deals with the calculation of the relations between the parameters of plasma and a toroidal resonator. It follows on from a previous paper (ÍCHA M: Czech. J. Phys.B 12 (1962), 632), where a simplified calculation of the sought relation is given.     

Dislocation arrangements during cyclic loading of pure iron

Fatigue induced substructure has been studied in polycrystalline iron (99.95 per cent) cycled at constant low stress amplitude. The main experimental technique was transmission electron microscopy. The results showed the dominant role of friction stress during cyclic loading and the importance of cross slip during dynamic recovery.     

Synthesis of new amphiphilic dendrons bearing aliphatic hydrocarbon surface sectors and a monocarboxylic or dicarboxylic acid focal point

[structure: see text]. A new series of amphiphilic G1-G3 dendrons containing purely aliphatic hydrocarbon dendritic surface sectors and one or two carboxylic acid group(s) at the focal point was synthesized in good yields. The key branching steps involve diallylation reactions of diethyl malonate or Meldrum's acid. These dendrons are highly soluble in hexane despite having highly polar carboxylic acid groups at the focal point.     

A boundary element method for homogenization of periodic structures

Homogenized coefficients of periodic structures are calculated via an auxiliary partial differential equation in the periodic cell. Typically, a volume finite element discretization is employed for the numerical solution. In this paper, we reformulate the problem as a boundary integral equation using Steklov–Poincaré operators. The resulting boundary element method only discretizes the boundary of the periodic cell and the interface between the materials within the cell. We prove that the homogenized coefficients converge super-linearly with the mesh size, and we support the theory with examples in two and three dimensions.     

Improved Decay for Solutions to the Linear Wave Equation on a Schwarzschild Black Hole

We prove that sufficiently regular solutions to the wave equation ${\square_g\phi=0}We prove that sufficiently regular solutions to the wave equation \square_gf = 0{\square_g\phi=0} on the exterior of the Schwarzschild black hole obey the estimates |f| ￡ C_d v₊^-\frac32+d{|\phi|\leq C_\delta v_+^{-\frac{3}{2}+\delta}} and |?_tf| ￡ C_d v₊^-2+d{|\partial_t\phi|\leq C_{\delta} v_+^{-2+\delta}} on a compact region of r, including inside the black hole region. This is proved with the help of a new vector field commutator that is analogous to the scaling vector field on Minkowski spacetime. This result improves the known decay rates in the region of finite r and along the event horizon.     

An axiomatization for the linear logic of knowledge and time LTK r with intransitive time relation

We study the problem of the axiomatization of the linear multimodal logic of knowledge and time LTK _r with reflexive intransitive time relation. The logic is defined semantically as the set of formulas true on frames of a special kind. The LTK _r -frames are linear chains of clusters connected by a reflexive intransitive relation R _T which simulates time. Elements inside a cluster are connected by several equivalence relations imitating the knowledge of different agents. The main result of the article is the proof of the fact that the finite set of formulas proposed by the authors is an axiomatization of the logic LTK _r with reflexive intransitive time relation.     

Analysis of formulas for calculating the main characteristics of backscattered electrons and how they compare to experimental results

Semiempirical relations for the following basic parameters of backscattered electrons in a scanning electron microscope are derived: reflection coefficient; average and most probable energies; energy spectra; and energy of backscattered electrons, depending on the angle of exit. The energy dependence is shown to have a maximum in the angular region of backscattered electrons Θ = 65°–75°.     

Structure and NMR properties of 6‐substituted‐5,6‐dihydrobenzo[c]phenanthridine alkaloids

We report a preparation of new 6‐substituted‐5,6‐dihydrobenzo[c]phenanthridines by the reaction of azoles with quaternary benzo[c]phenanthridine alkaloids sanguinarine and chelerythrine. The prepared compounds have been characterized by NMR spectroscopy, mass spectrometry, and single‐crystal X‐ray diffraction. Conformational behaviors of carbazole derivatives in solution have been investigated by low‐temperature NMR experiments. Barriers to rotation around newly formed C6–N bonds were determined to be 12–13 kcal/mol. Quantum chemical calculations have been used to reproduce the experimental observations. Large structural effects on several ¹H NMR resonances were observed experimentally, analyzed by Density Functional Theory (DFT) calculations at B3LYP/6‐311+G(d,p)/PCM level, and interpreted by ring‐current effects of the benzo[c]phenanthridine and carbazole units. Copyright © 2013 John Wiley & Sons, Ltd.