On the S-procedure and Some Variants

We give a concise review and extension of S-procedure that is an instrumental tool in control theory and robust optimization analysis. We also discuss the approximate S-Lemma as well as its applications in robust optimization.The many suggestions and detailed corrections of an anonymous referee are gratefully acknowledged.     

Development and Validation of a LC Method for the Analysis of Phenolic Acids in Turkish Salvia Species

An accurate, simple, reproducible, and sensitive method for determination of rosmarinic, caffeic, chlorogenic, and gallic acids in 12 Salvia species growing naturally in Anatolia, has been developed and validated. The phenolic acids were separated using a μBondapack C₁₈ column by gradient elution with a flow rate of 1.0 mL min⁻¹, which was adjusted to deliver firstly o-phosphoric acid 0.085% in water, 0.085% in methanol, and 0.085% in 2-propanol (80:10:10, v/v/v), then decreased gradually (60:20:20, v/v/v) during 20 min with a flow rate of 1.0 mL min⁻¹. The samples were monitored at 220 nm for gallic acid and 330 nm for rosmarinic, caffeic, and chlorogenic acids using photo-diode array detection. The linear range of detection for gallic, chlorogenic, caffeic, and rosmarinic acids were between 0.051–101.4, 0.207–103.6, 0.100–100, and 0.201–100.5 μg mL⁻¹, respectively. The linearity, range, peak purity, selectivity, system performance parameters, precision, accuracy, and robustness had also acceptable values. The developed method was applied to the flower, leaf, stem, and root parts of the Salvia species.

     

On-line preconcentration and determination of Au(III) in various environmental/industrial samples by flame atomic absorption spectrometry

A rapid and simple on-line method is described for the determination of Au(III) in various samples. The method is based on the sorption of gold(III) on Lewatit MonoPlus TP207 chelating resin including the iminodiacetate group, which is used as sorbent material and packed in a minicolumn. The chemical variables such as the pH of the sample solution, eluent type, interfering ions and concentrations of reagents, and instrumental variables such as sample loading volume, reagents flow rates, and tubing length, which affect the efficiency of the method were studied and optimised. Au(III) was sorbed on the chelating resin, from which it could be eluted with 3 mol L^?1 HCl, and then introduced directly to the nebuliser-burner system of FAAS. The limit of detection of the method was 0.2 µg L^?1 while the relative standard deviation was <4.0% for 20 µg L^?1 Au(III) concentration. The preconcentration factor was found to be 106 while the optimised sample volume was 15.3 mL. The accuracy of the method was verified by analysing the certified reference material. The developed method was applied successfully for the determination of gold in different samples with satisfactory results.     

Synthesis and Characterization of New Chelating Resin: Adsorption Study of Copper(II) and Chromium (III) Ions

Acrylamide based monomer, 5-methyl-2-thiozyl methacrylamide (MTMAAm) was synthesized by the reaction of 2-Amino-5-methyl thiazole with methacryloyl chloride in the presence of triethylamine(NR₃) at 0–5°C. The monomer MTMAAm was characterized by FT-IR and ¹H-and ¹³C-NMR spectral studies. A new chelating resin, poly(5-methyl-2-thiozyl methacrylamide-co-2-acrylamido-2-methyl-1-propanesulfonic acid-co-divinylbenzene) [MTMAAm/AMPS/DVB] was synthesized. This resin was characterized by FT-IR. In order to determine the adsorption behavior of chelating resin, the adsorption isotherm of Cr(III) and Cu(II) were studied. It was found that the adsorption isotherm of the ions fitted with Langmuir-type isotherms. From the Langmuir equation, the adsorption capacity of chelating resin for Cr(III) and Cu(II) was found to be 7.77 mg g^{? 1} and 4.27 mg g^{? 1}, respectively. Binding equilibrium constant was calculated to be 0.155 L mg^{? 1} and 0.106 L mg^{? 1} for Cu(II) and Cr(III), respectively.     

Lipase biosensor for tributyrin and pesticide detection

Potentiometric biosensors based on Candida rugosa lipase was described for the detection of organophosphorus pesticide; methyl-parathion and tributyrin. Lipase was immobilized on the glass electrode by means of a gelatin membrane, which is then cross-linked with glutaraldehyde. The principle of the biosensor is based on the measurement of pH variation which was recorded in millivolts due to the enzymatic hydrolysis of tributyrin to butyric acid. For the inhibitor detection, biosensor responses were measured after pesticide treatment, which caused a drop in enzyme activity because of the irreversible inhibition. Reactivation conditions of the reused enzyme electrodes were also investigated by pyridine-2-aldoxime methiodide (2-PAM). The limit of detection for tributyrin was estimated as 93?µM for lipase sensor within the linear range of 65–455?µM.     

Selective back-extraction and preconcentration of zinc(II) from metal-1,3,5-triketone extracts prior to its determination by flame atomic absorption spectrometry

A simple back-extraction method was developed for the separation and preconcentration of trace levels of zinc from different matrices. Ethyl-2-(4-methoxybenzoyl)-3-(4-methoxyphenyl)-3-oxopropanoylcarbamate (EMPC) was used as a new complexing agent for the extraction of zinc(II) from the aqueous sample phase to the methyl isobutyl ketone (MIBK) phase as Zn(EMPC)₂ complexes. The Zn(II) can be selectively stripped with 1?mL of 0.5?mol?L^?1 HCl from Mⁿ⁺(EMPC)_n complexes [Ag(I), Al(III), Cd(II), Cr(III), Cu(II), Fe(II), Fe(III), Mn(II), Ni(II), Pb(II) and Pd(II)] which dissolved in MIBK phase. Some experimental parameters, which are important for the whole extraction process, including pH, sample volume, shaking time, amount of the EMPC reagent, amount of MIBK, ionic strength, and type of back-extractant were investigated. The recovery for Zn(II) was greater than 95%. The detection limit of the method was found to be 0.2?µg?L ^{? 1} and the relative standard deviation as 6.4%. The concentrations of Zn(II) in the certified reference materials (LGC6019 river water and NIST-1547 peach leaves) by the presented method were in good agreement with the certified values. The proposed method was succesfully applied to the determination of zinc in some natural waters, rice, hair, soil, and tea samples.     

Stability and bifurcations analysis of a competition model with piecewise constant arguments

In this paper, we investigate local and global asymptotic stability of a positive equilibrium point of system of differential equations where t ≥ 0, the parameters r₁, k₁, α₁, α₂, r₂, k₂, and d₁ are positive, and [t] denotes the integer part of t ∈ [0, ∞ ). x(t) and y(t) represent population density for related species. Sufficient conditions are obtained for the local and global stability of the positive equilibrium point of the corresponding difference system. We show through numerical simulations that periodic solutions arise through Neimark–Sacker bifurcation. Copyright © 2014 John Wiley & Sons, Ltd.     

Discrete-Time Pricing and Optimal Exercise of American Perpetual Warrants in the Geometric Random Walk Model

An American option (or, warrant) is the right, but not the obligation, to purchase or sell an underlying equity at any time up to a predetermined expiration date for a predetermined amount. A perpetual American option differs from a plain American option in that it does not expire. In this study, we solve the optimal stopping problem of a perpetual American option (both call and put) in discrete time using linear programming duality. Under the assumption that the underlying stock price follows a discrete time and discrete state Markov process, namely a geometric random walk, we formulate the pricing problem as an infinite dimensional linear programming (LP) problem using the excessive-majorant property of the value function. This formulation allows us to solve complementary slackness conditions in closed-form, revealing an optimal stopping strategy which highlights the set of stock-prices where the option should be exercised. The analysis for the call option reveals that such a critical value exists only in some cases, depending on a combination of state-transition probabilities and the economic discount factor (i.e., the prevailing interest rate) whereas it ceases to be an issue for the put.     

Determination of some trace metal ions in various samples by FAAS after separation/preconcentration by copper(II)-BPHA coprecipitation method

A separation/preconcentration procedure based on the coprecipitation of Pb(II), Fe(III), Co(II), Cr(III) and Zn(II) ions with copper(II)-N-benzoyl-N-phenyl-hydroxylamine complex (Cu-BPHA) has been developed. The analytical variables including pH, amount of BPHA, amount of copper(II) as carrier element, and sample volume were investigated for the quantitative recoveries of the elements. No interfering effects were observed from the concomitant ions when present in real samples. The recoveries of the analyte ions were in the range of 95–100%. The detection limits (3 s) for Pb(II), Co(II), Fe(III), Cr(III) and Zn(II) ions were found to be 2.3, 0.7, 0.7, 0.3 and 0.4 µg L^?1, respectively. The validation of the procedure was performed by the analysis of CRM (SRM NIST-1547 peach leaves and LGC6019 river water) standard reference materials. The method was applied to the determination of the analytes in real samples including natural waters, hair, urine, soil, sediment and peritoneal fluids samples etc., and good results were obtained (relative standard deviations <4%, recoveries >95%).