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.     

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.     

Multilinear mappings and estimates of multiplicity

A method for estimating multiplicity of operators in terms of certain multilinear mappings is introduced. Several applications are given which include the following result: IfT is a completely non-unitary contraction on a complex Hilbert space, and for some vectorx ₀, then there exists a constant >0, such that for every positive integern, the multiplicity of the operatorT ⁿ is not less thann. This extends a result of B. Sz. Nagy and Foia [10].     

Microwave-assisted selective preparation and characterization of Li21Si5 and Li17Sn4

Two types of intermetallic lithium alloys, Li₂₁Si₅ and Li₁₇Sn₄ (previously Li₂₂Si₅ and Li₂₂Sn₅), were prepared for the first time using microwave-assisted solid-state reaction. The optimum oven power for their preparation is 80-60%, and the irradiation times are 5 min for Li₂₁Si₅ or 10 min for Li₁₇Sn₄. A cheap alumina crucible was found to be the most suitable container in quick (less than 10 min) microwave reactions for Li-containing alloys. The synthesized compounds were characterized by PXRD. Mössbauer spectroscopy was used to characterize Li₁₇Sn₄ under different conditions. The hyperfine interaction parameters of ¹¹⁹Sn in Li₁₇Sn₄ show a typical Li-Sn alloy Sn isomer shift (1.88 mm/s). The oxidization processes of the two intermetallic lithium alloys in air were investigated. The microwave method was found to be simple, fast and efficient, with high selectivity for the preparation of these compounds.     

Magnetic circular dichroism of I2 in the cordes band energy region

The absorption and magnetic circular dichroism (MCD) of iodine in the gas phase was recorded over the wavelength range 1950-1780 Å. The strong MCD si     

Adjustable robust counterpart of conic quadratic problems

This paper presents an approximate affinely adjustable robust counterpart for conic quadratic constraints. The theory is applied to obtain robust solutions to the problems of subway route design with implementation errors and a supply chain management with uncertain demands. Comparison of the adjustable solutions with the nominal and non-adjustable robust solutions shows that the adjustable (dynamic) robust solution maintains feasibility for all possible realizations, while being less conservative than the usual (static) robust counterpart solution.     

[All]-S,S-dioxide Oligo-Thienylenevinylenes: Synthesis and Structural/Electronic Shapes from Their Molecular Force Fields

Oligo-S,S-dioxothienylenevinylenes have been prepared by transferring oxygen atoms to the sulfur atoms using the HOF ⋅ CH₃CN complex. Their photophysical properties are presented in comparison with their thiophenevinylene congeners. Together with their vibrational properties and molecular force fields, this study allows for the interpretation of the alteration of aromaticity and inter-ring exocyclic π-conjugation in this series.     

A Bragg grating embedded in a slab waveguide fabricated by the implantation of high-energy light ions in KLTN substrate

Electro-optically tunable transmission grating was imprinted in potassium lithium tantalate niobate by irreversible spatial patterning of the dielectric constant. While embedded into waveguided architecture, it provides a reliable and versatile building block for opto-electronic circuitry, capable of both active switching and multiplexing. Realization of such a block is critical for the fabrication of integrated photonic circuits in electro-optic substrates by means of Refractive Index Engineering by fast ion implantation.     

Impact of growth kinetics on morphology and pore structure of TiO2-one-pot synthesis of macroporous TiO2 microspheres

Titanium dioxide was synthesized by the hydrolysis of titanium tetraisopropoxide (TTIP) in the presence of acetic acid, 2-propanol, and organic amines (octylamine, aniline, and isobutylamine). H2O was supplied by an esterification reaction between acetic acid and 2-propanol (denoted as H2Oe), and/or by intentionally adding it (denoted as H2Oa). It was found that the quantity of H2Oa plays a crucial role in the morphology and porous structure of the final TiO2 product. Without the addition of H2Oa, 1D and porous TiO2 was synthesized. With the addition of H2Oa, and when the H2Oa:TiO2 molar ratio was in the range of 1:1 to 60:1, macroporous TiO2 microspheres possessing a large surface area and high thermal stability were obtained. When the H2Oa:TiO2 molar ratio exceeded 60:1, porous TiO2 with an irregular shape was formed. The variation in the morphology and porous structure is attributed to the manipulation of the growth kinetics by the addition of water.