Hausdorff continuity of approximate solution maps to parametric primal and dual equilibrium problems

In this paper, we consider parametric primal and dual equilibrium problems in locally convex Hausdorff topological vector spaces. Sufficient conditions for the approximate solution maps to be Hausdorff continuous are established. We provide many examples to illustrate the essentialness of the imposed assumptions. As applications of these results, the Hausdorff continuity of the approximate solution maps for optimization problems, variational inequalities and fixed-point problems are derived.     

General financial market model defined by a liquidation value process

Financial market models defined by a liquidation value process generalize the conic models of Schachermayer and Kabanov where the transaction costs are proportional to the exchanged volumes of traded assets. The solvency set of all portfolio positions that can be liquidated without any debt is not necessary convex, e.g. in presence of proportional transaction costs and fixed costs. Therefore, the classical duality principle based on the Hahn–Banach separation theorem is not appropriate to characterize the prices super hedging a contingent claim. Using an alternative method based on the concepts of essential supremum and maximum, we provide a characterization of European and American contingent claim prices under the absence of arbitrage opportunity of the second kind.     

Continuous‐scan capability at SSRL and applications to X‐ray diffraction

Typical X‐ray diffraction measurements are made by moving a detector to discrete positions in space and then measuring the signal at each stationary position. This step‐scanning method can be time‐consuming, and may induce vibrations in the measurement system when the motors are accelerated and decelerated at each position. Furthermore, diffraction information between the data points may be missed unless a fine step‐scanning is used, which further increases the total measurement time. To utilize beam time efficiently, the motor acceleration and deceleration time should be minimized, and the signal‐to‐noise ratio should be maximized. To accomplish this, an integrated continuous‐scan system was developed at the Stanford Synchrotron Radiation Lightsource (SSRL). The continuous‐scan system uses an in‐house integrated motor controller system and counter/timer electronics. SPEC software is used to control both the hardware and data acquisition systems. The time efficiency and repeatability of the continuous‐scan system were tested using X‐ray diffraction from a ZnO powder and compared with the step‐scan technique. Advantages and limitations of the continuous‐scan system and a demonstration of variable‐velocity continuous scan are discussed.     

Diffusion of non-volatile phenolic compounds in zeolite beta and silicalite in liquid phase

The present study aims to systematically investigate the adsorption kinetics of “non-volatile” phenolic compounds with different critical diameters (p-coumaric acid, ferulic acid, sinapinic acid, p-hydroxybenzoic acid, vanillic acid, syringic acid, and vanillin) onto zeolite beta and silicalite in several solvents. In the aqueous phase, the corrected diffusivity of non-volatile phenolic compounds is 2–5 orders of magnitude smaller than that of volatile aromatic compounds with the same critical diameter. On the other hand, the corrected diffusivity in zeolite beta is on the same order of magnitude among non-volatile phenolic compounds, despite the significant difference in critical diameter of the adsorbate. This suggests that the intracrystalline diffusivity of the non-volatile adsorbate is strongly affected by its original molecular immobility, rather than by the size (narrowness) of the adsorbate and micropore aperture. Non-volatility is considered to remarkably lower the molecular mobility of adsorbate on the surface of zeolite, even in the liquid phase. In addition, the intracrystalline diffusivity of non-volatile adsorbate is strongly affected by the type of solvent, and a close correlation was found between intracrystalline diffusivity and adsorption affinity. Revelations as to the kinetic behavior of non-volatile adsorbate in zeolite are expected to supply more information on the kinetic separation of compounds in the liquid phase. The significant difference in diffusivity among non-volatile and volatile adsorbates in zeolite leads to the possibility of kinetic separation among these adsorbates.     

Magnetic ionic liquids as non-conventional extraction solvents for the determination of polycyclic aromatic hydrocarbons

This work describes the applicability of magnetic ionic liquids (MILs) in the analytical determination of a group of heavy polycyclic aromatic hydrocarbons. Three different MILs, namely, benzyltrioctylammonium bromotrichloroferrate (III) (MIL A), methoxybenzyltrioctylammonium bromotrichloroferrate (III) (MIL B), and 1,12-di(3-benzylbenzimidazolium) dodecane bis[(trifluoromethyl)sulfonyl)]imide bromotrichloroferrate (III) (MIL C), were designed to exhibit hydrophobic properties, and their performance examined in a microextraction method for hydrophobic analytes. The magnet-assisted approach with these MILs was performed in combination with high performance liquid chromatography and fluorescence detection. The study of the extraction performance showed that MIL A was the most suitable solvent for the extraction of polycyclic aromatic hydrocarbons and under optimum conditions the fast extraction step required ∼20 μL of MIL A for 10 mL of aqueous sample, 24 mmol L⁻¹ NaOH, high ionic strength content of NaCl (25% (w/v)), 500 μL of acetone as dispersive solvent, and 5 min of vortex. The desorption step required the aid of an external magnetic field with a strong NdFeB magnet (the separation requires few seconds), two back-extraction steps for polycyclic aromatic hydrocarbons retained in the MIL droplet with n-hexane, evaporation and reconstitution with acetonitrile. The overall method presented limits of detection down to 5 ng L⁻¹, relative recoveries ranging from 91.5 to 119%, and inter-day reproducibility values (expressed as relative standard derivation) lower than 16.4% for a spiked level of 0.4 μg L⁻¹ (n = 9). The method was also applied for the analysis of real samples, including tap water, wastewater, and tea infusion.     

Analysis and deconvolution of dimethylnaphthalene isomers using gas chromatography vacuum ultraviolet spectroscopy and theoretical computations

An issue with most gas chromatographic detectors is their inability to deconvolve coeluting isomers. Dimethylnaphthalenes are a class of compounds that can be particularly difficult to speciate by gas chromatography – mass spectrometry analysis, because of their significant coelution and similar mass spectra. As an alternative, a vacuum ultraviolet spectroscopic detector paired with gas chromatography was used to study the systematic deconvolution of mixtures of coeluting isomers of dimethylnaphthalenes. Various ratio combinations of 75:25; 50:50; 25:75; 20:80; 10:90; 5:95; and 1:99 were prepared to test the accuracy, precision, and sensitivity of the detector for distinguishing overlapping isomers that had distinct, but very similar absorption spectra. It was found that, under reasonable injection conditions, all of the pairwise overlapping isomers tested could be deconvoluted up to nearly two orders of magnitude (up to 99:1) in relative abundance. These experimental deconvolution values were in agreement with theoretical covariance calculations performed for two of the dimethylnaphthalene isomers. Covariance calculations estimated high picogram detection limits for a minor isomer coeluting with low to mid-nanogram quantity of a more abundant isomer. Further characterization of the analytes was performed using density functional theory computations to compare theory with experimental measurements. Additionally, gas chromatography – vacuum ultraviolet spectroscopy was shown to be able to speciate dimethylnaphthalenes in jet and diesel fuel samples.     

Characterization of conformers and dimers of antithrombin by capillary electrophoresis-quadrupole-time-of-flight mass spectrometry

Antithrombin (AT) is a plasma glycoprotein which possesses anticoagulant and anti-inflammatory properties. AT exhibits various forms, among which are native, latent and heterodimeric ones. We studied the potential of capillary electrophoresis-mass spectrometry (CE-MS) using a sheath liquid interface, electrospray ionization (ESI), and a quadrupole-time-of-flight (Q-TOF) mass spectrometer to separate and quantify the different AT forms. For CE separation, a neutral polyvinyl alcohol (PVA) coated capillary was employed. The protein conformation was preserved by using a background electrolyte (BGE) at physiological pH. A sheath liquid of isopropanol-water 50:50 (v/v) with 14 mM ammonium acetate delivered at a flow rate of 120 μL h⁻¹ resulted in optimal signal intensities. Each AT form exhibited a specific mass spectrum, allowing unambiguous distinction. Several co-injection experiments proved that latent AT had a higher electrophoretic mobility (μ_ep) than native AT, and that these conformers could associate to form a heterodimer during the CE analysis. The developed CE-MS method enabled the detection and quantitation of latent and heterodimeric forms in a commercial AT preparation stored at room temperature for three weeks.     

Synthesis,Characterization, and Anticancer Activities of Pyrogallol‐Based Arylspiroborates

Arylspiroborate salts derived from pyrogallol, gallic acid, and propyl gallate have been prepared and characterized fully, including an X‐ray diffraction study for the tetrabutylammonium gallic acid complex 4 . The tetrabutylammonium salts were examined for their potential anticancer activities against renal cell carcinoma (RCC) cell lines, using NBu₄[Bcat₂] (cat = catecholato) as a control.     

Validated multi‐drug determination using liquid chromatography with tandem mass spectrometry for the evaluation of a commercial drug disposal product

Currently, there are limited effective means of drug disposal for consumers, and this creates a gateway to illicit use and environmental contamination. Here, we evaluated the efficacy of a new drug disposal product, composed from a slurry of activated carbon, which claims to sequester up to 100% of a drug's active ingredient when the loading capacity is not exceeded, making it safe to dispose in landfill. High‐performance liquid chromatography with tandem mass spectrometry was applied to quantify as many as 24 drugs (opiates, barbiturates, statins, amphetamine, and benzodiazepine drugs) in the residual solvent solution from the product. Calibration curves were established in the concentration ranges of 0.25–7.0 μg/mL and showed good linearity. The limits of detection varied from 0.001 to 0.02 μg/mL, depending on the drug. Accuracy ranged from 80 to 111% for quality control samples, with a few minor exceptions. Precision overall varied between 0.2 to 12.7%. In sample bottles tested, where active ingredient of the loaded drug was below the maximum sorption capacity stated on the label, 98 to >99.9% of the active ingredient was sequestered. Percent active ingredient adsorbed was slightly lower in bottles loaded in excess of label specifications.     

Visible Light Activation of Boronic Esters Enables Efficient Photoredox C(sp2)–C(sp3) Cross‐Couplings in Flow

We report herein a new method for the photoredox activation of boronic esters. Using these reagents, an efficient and high‐throughput continuous flow process was developed to perform a dual iridium‐ and nickel‐catalyzed C(sp²)–C(sp³) coupling by circumventing solubility issues associated with potassium trifluoroborate salts. Formation of an adduct with a pyridine‐derived Lewis base was found to be essential for the photoredox activation of the boronic esters. Based on these results we were able to develop a further simplified visible light mediated C(sp²)–C(sp³) coupling method using boronic esters and cyano heteroarenes under flow conditions.