OBSERVATIONS ON INFEASIBILITY DETECTORS FOR CLASSIFYING CONIC CONVEX PROGRAMS

Abstract

New insights are presented from a convex duality classification theory of over 25 years ago for recent computational complexity results developed for recognizing some of the asymptotic duality states that prevail for an arbitrary convex programming pair.     

Polytopal estimate of Mirkovi?–Vilonen polytopes lying in a Demazure crystal

In this paper, we give a polytopal estimate of Mirkovi?–Vilonen polytopes lying in a Demazure crystal in terms of Minkowski sums of extremal Mirkovi?–Vilonen polytopes. As an immediate consequence of this result, we provide a necessary (but not sufficient) polytopal condition for a Mirkovi?–Vilonen polytope to lie in a Demazure crystal.     

Fluorinated Porous Poly(spirobifluorene) Via Direct C‒H Arylation: Characterization,Porosity, and Gas Uptake

Considering intrinsic properties of conjugated polyfluorenes and special functions of porous polymers, synthesis of fluorinated porous poly(spirobifluorene) via direct C?H arylation polycondensation is explored. Owing to the contorted structure and cross-linking nature, the obtained polymer FPSBF shows permanent porosities with Brunauer–Emmett–Teller specific surface area up to 700 m² g^?1 and exhibits a narrow pore size distribution with the dominant pore size at about 0.63 nm, which is more suitable for adsorption of small gas molecules. Based on the measured gas physisorption isotherms with pressure up to 1.13 bar, the obtained polymer shows good uptaking capacities for hydrogen (1.30 wt% at 1.0 bar and 77 K) and methane (4.80 wt% 1.0 bar and 273 K). Moreover, FPSBF has significant adsorption selectivity for CH₄ against N₂ and the estimated ideal adsorption selectivity ratio is up to 30/1 at 1.0 bar and 273 K, which makes the material possess potential application in gas separation.     

The Effect of Oxygen on Conversion in the Organic Peroxide-initiated High-Pressure Polymerization of Ethylene

To initiate the high-pressure polymerization of ethylene, oxygen is used together with organic peroxides in a number of tubular reactor processes. Since molecular oxygen is capable of promoting or inhibiting radical polymerization, depending on the reaction conditions chosen, controlled experiments were carried out to clarify these aspects of high pressure ethylene polymerization. In continuous polymerization tests carried out at 1700 bar and temperatures between 110 and 320°C, conversions were determined with tert-amyl perneodecanoate and di-tert-butyl peroxide initiation in the presence of various quantities of oxygen. Batch tests using a photo-initiator together with oxygen were also carried out. A comparison with polymerizations under conditions of careful elimination of oxygen shows no effect on the peroxide-initiated polymerization up to temperatures of 160 to 170°C. Although oxygen is an initiator at higher temperatures, the conversions obtained from the simultaneous addition of controlled quantities of oxygen and organic peroxides is lower than that obtained by adding together the conversions from the separate polymerizations.     

Polarity and steric effect of the lateral substituent on the mesophase behaviour of some newly prepared liquid crystals

Eight homologous series of 2- (or 3-) substituted phenyl 4?-(4?-alkoxy phenylazo) benzoates (In_a–h) were prepared in which, within each homologous series, the length of the terminal alkoxy group varies between 6, 8, 10 and 12 carbons, while the other substituent, X, is a laterally attached polar group that alternatively changed from CH₃, H, F, Br and CN. Compounds prepared were characterised by infrared and ¹H-NMR spectroscopy, and their mesophase behaviour investigated by differential scanning calorimetry and identified by polarised light microscopy. The results were discussed in terms of polarity and steric effects. The stability of the mesophase was correlated once with the dipolar anisotropy of the whole molecule and another with the dipolar anisotropy of the substituent, X. A comparative study was made between the investigated compounds and their previously prepared linear 4-substituted isomers, namely 4-substituted phenyl 4?-(4?-alkoxy phenylazo) benzoates (In_i–k).     

Ligandless-ultrasound-assisted emulsification microextraction followed by inductively coupled plasma-optical emission spectrometry for simultaneous determination of heavy metals in water samples

In this study, a simple and efficient method of ligandless-ultrasound-assisted emulsification microextraction (LL-USAEME) followed by inductively coupled plasma-optical emission spectrometry (ICP-OES) has been developed for simultaneous extraction, preconcentration and determination of manganese, cadmium, cobalt and nickel in water samples. In the proposed approach, tetrachloroethylene was selected as extraction solvent. The effect of important experimental factors such as volume of extraction solvent, pH, sonication time, salt concentration, and temperature was investigated by using a fractional factorial design (2^5?1) to identify important factors and their interactions. In the next step, a Box-Behnken design (BBD) was applied for optimisation of significant factors. The obtained optimal conditions were: 30?µL for extraction solvent, 12 for pH, 5?min for sonication time, and 5% w/v for salt concentration. The limits of detections (LODs) for Cd(II), Co(II), Mn(II) and Ni(II) were 0.20, 0.13, 0.21 and 0.28?µg?L^?1, respectively. Relative standard deviations (RSD, C?=?200.0?µg?L^?1, n?=?9) were between 3.4–7.5% and the calibration graphs were linear in the range of 0.25 to 1000.0?µg?L^?1 for Mn, 0.5–1000.0?µg?L^?1 for Co and Ni and 1.0–250.0?µg?L^?1 for Cd. The determination coefficients (R ²) of the calibration curves for the analytes were in the range of 0.993 to 0.999. The proposed method was validated by using two certified reference materials, and also the method was applied successfully for the determination of heavy metals in different real water samples.