Semidefinite programming hierarchies for constrained bilinear optimization

Mathematical Programming - We give asymptotically converging semidefinite programming hierarchies of outer bounds on bilinear programs of the form $${\mathrm {Tr}}\big [H(D\otimes E)\big ]$$ ,...     

Ionic liquids extraction of Para Red and Sudan dyes from chilli powder, chilli oil and food additive combined with high performance liquid chromatography

A simple analytical method, based on the coupling of ionic liquid-based extraction with high performance liquid chromatography (HPLC), is developed for the determination of Sudan dyes (I, II, III and IV) and Para Red in chilli powder, chilli oil and food additive samples. Two ionic liquids (ILs), 1-butyl-3-methylimidazolium hexafluorophosphate ([C₄mim][PF₆]) and 1-octyl-3-methylimidazolium hexafluorophosphate ([C₈mim][PF₆]), were compared as extraction solvents; experiments indicated that the latter possesses higher recoveries for each analyte. Parameters related to extraction of Sudan dyes and Para Red were also optimized. Under the optimal conditions, good reproducibility of extraction performance was obtained, with the relative standard deviation (RSD) values ranging from 2.0% to 3.5%. The detection limits of Sudan dyes and Para Red (LOD, S/N = 3) were in the range of 7.0-8.2 μg kg⁻¹ for chilli powder and 11.2-13.2 μg L⁻¹ for chilli oil and food additive. The recoveries were in the range of 76.8-109.5% for chilli powder samples and 70.7-107.8% for chilli oil and food additive samples.     

Effect of magnetostrictive phase on structural, dielectric and electrical properties of NiFe2O4 + Pb0.93La0.07(Zr0.60Ti0.40)O3 composites

Particulate composites of NiFe₂O₄ (NFO) and Pb_0.93La_0.07 (Zr_0.60Ti_0.40) O₃ (PLZT) were synthesized by solid-state reaction technique. Structure and surface morphological studies were carried out using X-ray diffraction and scanning electron microscopy techniques, respectively. Frequency dependent variation of dielectric constant (), loss tangent (tan δ) and ac resistivity for (x) NFO + (1−x) PLZT composites in the range 100 Hz–5 MHz at room temperature were studied. The temperature dependence of dielectric constant (′), loss tangent (tan δ) was studied in wide temperature range of measurement at fixed frequencies. Also DC resistivity measurements were carried out in the temperature range of 300 K–923 K. Structural, dielectric and electrical properties show notable change due to presence of magnetostrictive NFO phase along with PLZT.     

Depth Properties of scaled attachment random recursive trees

We study depth properties of a general class of random recursive trees where each node i attaches to the random node \begin{align*}\left\lfloor iX_i\right\rfloor\end{align*} and X₀,…,X_n is a sequence of i.i.d. random variables taking values in [0,1). We call such trees scaled attachment random recursive trees (sarrt). We prove that the typical depth D_n, the maximum depth (or height) H_n and the minimum depth M_n of a sarrt are asymptotically given by D_n ～μ^‐1 log n, H_n ～ α_max log n and M_n ～ α_min log n where μ,α_max and α_min are constants depending only on the distribution of X₀ whenever X₀ has a density. In particular, this gives a new elementary proof for the height of uniform random recursive trees H_n ～ elog n that does not use branching random walks.© 2011 Wiley Periodicals, Inc. Random Struct. Alg., 2011     

Spectrophotometric and Atomic Absorption Spectroscopic Determination of Some Fluoroquinolone Antibacterials by Ion‐pair Complex Formation with Bismuth (III) Tetraiodide

New simple spectrophotometric and atomic absorption spectrometric (AAS) methods have been developed for the determination of levofloxacin (I), norfloxacin (II), and ciprofloxacin (III) in pure form, tablet formulations, and spiked human urine. The methods are based on the formation of ion‐pair associates between the drugs and the inorganic complex, bismuth (III) tetraiodide. The reaction occurs in acidic medium to form orange‐red ion‐pair associates which are instantaneously precipitated. The formed precipitates are then filtered off and the residual unreacted metal complex in the filtrate is determined either spectrophotometrically at 453 nm or by AAS at 223.1 nm. Also, the precipitates may be dissolved in acetone and quantified spectrophotometrically at 469 nm or decomposed by hydrochloric acid, and the bismuth content is determined by AAS at 223.1 nm. The methods permit the determination of the three studied drugs in the range of 5–80 μg mL^?1. The proposed methods were successfully applied to determine these drugs in their tablet formulations and spiked urine samples without any evidence for interference from pharmaceutical additives or biological matrix. The results were in good agreement with those obtained by the reference methods. The proposed methods, especially if automated, can be confidently applied for quality control and routine analysis of the studied drugs.     

Isobaric-isothermal monte carlo simulations from first principles: application to liquid water at ambient conditions.

A series of first-principles Monte Carlo simulations in the isobaric-isothermal ensemble were carried out for liquid water at ambient conditions (T=298 K and p=1 atm). The Becke-Lee-Yang-Parr (BLYP) exchange and correlation energy functionals and norm-conserving Goedecker-Teter-Hutter (GTH) pseudopotentials were employed with the CP2 K simulation package to examine systems consisting of 64 water molecules. The fluctuations in the system volume encountered in simulations in the isobaric-isothermal ensemble require a reconsideration of the suitability of the typical charge-density cutoff and the regular grid-generation method previously used for the computation of the electrostatic energy in first-principles simulations in the microcanonical or canonical ensembles. In particular, it is noted that a much higher cutoff is needed and that the most computationally efficient method of creating grids can result in poor simulations. Analysis of the simulation trajectories using a very large charge-density cutoff at 1200 Ry and four different grid-generation methods point to a significantly underestimated liquid density of about 0.8 g cm-3 resulting in a somewhat understructured liquid (with a value of about 2.7 for the height of the first peak in the oxygen-oxygen radial distribution function) for BLYP-GTH water at ambient conditions. In addition, a simulation using a charge-density cutoff at 280 Ry yields a higher density of 0.9 g cm-3, showing the sensitivity of the simulation outcome to this parameter.     

Characterization of SnO2 obtained from the thermal oxidation of vacuum evaporated Sn thin films

Tin oxide has been prepared by thermal oxidation of evaporated tin thin films onto pyrex glass substrates. Films oxidation was achieved in air at a temperature of 600 °C with varied duration from 20min to 3 h. Structural, optical and electrical properties of the films were characterized by means of X-ray diffraction, UV–vis spectroscopy and electrical resistivity measurements respectively. The X-ray analysis revealed the transformation of Sn into SnO₂ with preferential orientation along (101) plans. No intermediate phases such as SnO and Sn₃O₄ were evidenced. It was also found that the SnO₂ crystallites orientation changed with the annealing time due to the strain energy effect. Both band gap energy and electrical resistivity decrease with annealing time due to the crystalline quality improvement and films densification. We have noticed that oxidation at 600 °C for 3 h leads to transparent and conductive films with suitable properties for photovoltaic applications.