Hidden convexity in some nonconvex quadratically constrained quadratic programming

We consider the problem of minimizing an indefinite quadratic objective function subject to twosided indefinite quadratic constraints. Under a suitable simultaneous diagonalization assumption (which trivially holds for trust region type problems), we prove that the original problem is equivalent to a convex minimization problem with simple linear constraints. We then consider a special problem of minimizing a concave quadratic function subject to finitely many convex quadratic constraints, which is also shown to be equivalent to a minimax convex problem. In both cases we derive the explicit nonlinear transformations which allow for recovering the optimal solution of the nonconvex problems via their equivalent convex counterparts. Special cases and applications are also discussed. We outline interior-point polynomial-time algorithms for the solution of the equivalent convex programs. This author's work was partially supported by GIF, the German-Israeli Foundation for Scientific Research and Development and by the Binational Science Foundation. This author's work was partially supported by National Science Foundation Grants DMS-9201297 and DMS-9401871.     

Growing ZnO crystals on magnetite nanoparticles

We report herein on the oriented growth of ZnO crystals on magnetite nanoparticles. The ZnO crystals were grown by hydrolyzing a supersaturated aqueous solution of zinc nitrate. The seeds for the growth were magnetite nanoparticles with a diameter of 5.7 nm and a narrow size distribution. Hollowed ZnO hexagons of 0.15 microm width and 0.5 microm length filled with Fe(3)O(4) particles were obtained. HR-TEM (high-resolution transmission electron microscopy) and selected-area EDS (energy-dispersive spectroscopy) show that the nanoparticles are homogenously spread in the ZnO tubes. Zeta potential measurements were employed to understand the relationship between the nanoparticles and the oriented growth of the ZnO crystals. The results show that the surfactants induced the directional growth of the ZnO crystals.     

Alkaline Metal Stannide‐Stannates: ‘Double Salts’ with Zintl Sn and Stannate SnO Anions

Using the reduction of tin oxides with the elemental alkaline metals rubidium and cesium, stannide stannates have been synthesized which contain Zintl anions [Sn₄]^4— (i.e. Sn^—I) and isolated oxostannate ions [SnO₃]^4— (i.e. Sn^+II) together with further oxide ions for charge compensation. The crystal structures of the three compounds A_23.6Sn_7.4O_13.2 = A_23.6[Sn₄][SnO₃]_3.4[O]₃ (A = Rb 1a : monoclinic, P2₁/c, a = 2174.2(6), b = 1137.0(6), c = 2373.6(6) pm, β = 116.11(2)°, Z = 4, R1 = 0.056; A = Cs 1b : monoclinic, P2₁/c, a = 2042.6(6), b = 1185.4(3), c = 2481.1(7) pm, β = 97.06(2)°, Z = 4, R1 = 0.075) and Cs₄₈Sn₂₀O₂₁ = Cs₄₈[Sn₄]₄[SnO₃]₄[O]₇[O₂] ( 2 monoclinic, P2/c, a = 1701.8(3), b = 877.4(2), c = 4556.9(7) pm, β= 101.47(1)°, R1 = 0.093) have been determined on the basis of single crystal data. The transparency of the compounds allowed the recording of raman spectra of the anion [Sn₄]^4—. The ¹¹⁹Sn Moessbauer spectrum of the rubidium compound shows a singulet in good agreement with RbSn, overlapping a doublet caused by Sn²⁺ in the asymmetrical environment of the strongly electronegative oxygen ligands of SnO.     

High-Resolution Solid-State MAS13C- and 1H-NMR Spectra of Benzenoid Aromatics Adsorbed on Alumina and Silica: Successful Applications of 1D and 2D Pulse Experiments from Liquid-State NMR

Strong line-narrowing effects in solid-state, magic-angle-spinning (MAS) ¹³C- as well as ¹H-NMR spectra of benzenoid aromatics adsorbed at alumina or silica surfAccs indicate high mobility of the organic adsorbates. Even under modest spinning rales (1 kHz), dipolar couplings are sufficiently reduced to allow scalar ^13C,¹H couplings to be measured. Hetero- and homonuclear pulse sequences known from high-resolution NMR in liquids, like SEFT, ^J-RESOLVED, DEPT, COSY, and ¹³C,¹H shift-correlation experiments are successfully applicable. ¹³C spin-lattice relaxation limes are as short as 0.5 s (CH) and 1.1 s (C_q), and T₁(¹H) values are in the order of 0.3 s.     

Reactions under autogenic pressure at elevated temperature (RAPET) of various alkoxides: formation of metals/metal oxides-carbon core-shell structures

The RAPET reaction at 700 degrees C, of different alkoxides (Ti, V, and Si) led to three different nanocomposites. Carbon is the element common to all three structures. Carbon was found as the core in the decomposition of TEOS, as the shell in the decomposition of VO(OEt)3 and embedded in, or mixed completely with, TiO2 in the decomposition of Ti(OiPr)4. This novel method using only metallic alkoxide precursor, in the absence of catalyst, leads in a one-step process to core-shell structures.