On uniqueness in inverse problems for semilinear parabolic equations

Communicated by R. V. Kohn     

Stereocontrolled alkylation of unsaturated compounds with alkoxytitanacyclopropane reagents

Interaction of titanium(IV) isopropoxide with ethylmagnesium bromide and its higher homologs leads to the generation of alkoxytitanacyclopropane species, which are able to act in the reactions with unsaturated compounds as 1,2‐dicarbanionic alkylating agents. The present review is focused on the processes of intermolecular regio‐ and stereoselective alkylation of carboxylic esters and allylic alcohol derivatives with alkoxytitanacyclopropane reagents. The oxophilicity of the titanium atom and its tendency to form sterically crowded ate complexes are probably the main factors providing a high level of selectivity of these transformations. © 2008 The Japan Chemical Journal Forum and Wiley Periodicals, Inc. Chem Rec 8: 269–278; 2008: Published online in Wiley InterScience ( www.interscience.wiley.com ) DOI 10.1002/tcr.20155     

Classical and quantum percolation phenomena and controlling them in eutectic semiconductor-superconductor compositions

Experimental data on the conduction of heterogeneous systems have been traditionally interpreted in the context of the theory of percolation phenomena taking into account the relative threshold volume fraction η_C ≈ 0.16) of the high-conductivity phase. This work is concerned with the conduction of eutectic compositions semiconductor-normal metal at T > T _c (the classical limit) and semiconductor-superconductor at T < T _c (the quantum limit) obtained at various material growth rates; these materials contain metal particles as oriented whiskers in semiconducting matrices. The paper presents spatial and energy models of discrete, finite, and infinite clusters that well explain classical and quantum percolation conductivities. Depending on the growth rate of eutectic compositions, their classical and quantum conductivities can manifest themselves at arbitrary percolation thresholds η_p (0 < η_p ≤ η_c). It is shown that the density of whiskers, the distances between them, their diameters, and the critical supercurrent density per whisker can be controlled by varying the rate of composition growth.     

Electro-optical properties of strontium-barium niobate crystals and their relation to the domain structure of the crystals

The electro-optical coefficients r _ij and half-wave voltage V_λ/2 of strontium-barium niobate crystals poled in the ferroelectric phase are shown to vary along the polar axis. The r _ij (z) and V_λ/2(z) dependences indicate the presence of a residual domain density D(z) and clearly depend on the sign of the polarizing field, with r _ij being minimum (D being maximum) near the negative electrode. This character of the D(z) distribution and, hence, the r _ij (z) and V_λ/2(z) coordinate dependences can be explained by predominant domain nucleation near the negative electrode, which is revealed when the switching processes are studied using 90° (Rayleigh) light scattering from domain walls.