A one‐dimensional computational model for hyperelastic string structures with Coulomb friction

In this paper, we consider a new model for the simulation of textiles with frictional contact between fibers and no bending resistance. In the model, one‐dimensional hyperelasticity and the Capstan equation are combined, and its connection with conventional hyperelasticity and Coulomb friction models is shown. Then, the model is formulated as a problem with the rate‐independent dissipation, and we prove that the problem possesses proper convexity and continuity properties. The article concludes with a numerical algorithm and provides numerical experiments along with a comparison of the results with a real measurement. Copyright © 2016 John Wiley & Sons, Ltd.     

Analytic approach to solve a degenerate parabolic PDE for the Heston model

We present an analytic approach to solve a degenerate parabolic problem associated with the Heston model, which is widely used in mathematical finance to derive the price of an European option on an risky asset with stochastic volatility. We give a variational formulation, involving weighted Sobolev spaces, of the second‐order degenerate elliptic operator of the parabolic PDE. We use this approach to prove, under appropriate assumptions on some involved unknown parameters, the existence and uniqueness of weak solutions to the parabolic problem on unbounded subdomains of the half‐plane. Copyright © 2017 John Wiley & Sons, Ltd.     

Lagrange Multipliers and mixed formulations for some inequality constrained variational inequalities and some nonsmooth unilateral problems

Abstract

This paper addresses a class of inequality constrained variational inequalities and nonsmooth unilateral variational problems. We present mixed formulations arising from Lagrange multipliers. First we treat in a reflexive Banach space setting the canonical case of a variational inequality that has as essential ingredients a bilinear form and a non-differentiable sublinear, hence convex functional and linear inequality constraints defined by a convex cone. We extend the famous Brezzi splitting theorem that originally covers saddle point problems with equality constraints, only, to these nonsmooth problems and obtain independent Lagrange multipliers in the subdifferential of the convex functional and in the ordering cone of the inequality constraints. For illustration of the theory we provide and investigate an example of a scalar nonsmooth boundary value problem that models frictional unilateral contact problems in linear elastostatics. Finally we discuss how this approach to mixed formulations can be further extended to variational problems with nonlinear operators and equilibrium problems, and moreover, to hemivariational inequalities.     

Pesticides as Microemulsion Formulations

Conventional systems like wettable powders, emulsifiable concentrates (ECs), oil in water emulsions (O/W emulsions), water in oil emulsions (W/O emulsions), aqueous suspension concentrates etc. are popularly used as the pesticide formulations. However, the microemulsion systems are preferred for their long-term thermodynamic stability, low viscosity, cost economy, and aesthetic appeal. Such systems provide a method for preparing an isotropic mixture of oil and water. Major advantage of microemulsion is in usage of the widely, easily available, environmentally friendly, and least expensive diluents, water. Formulation of pesticide microemulsion is a difficult task. The present investigation deals with the systematic study to arrive at the economical composition for microemulsion and solubilized systems. These compositions gave maximum stability with the optimum usage of surfactants. The microemulsion and solubilized systems when further diluted with water gave macroemulsion and microemulsion respectively, which were stable over an extended period of time.     

Determination of acidic pharmaceutical products and carbamazepine in roughly primary-treated wastewater by solid-phase extraction and gas chromatography–tandem mass spectrometry

A gas chromatography–tandem mass spectrometry (GC–MS/MS) method has been developed for the determination of selected pharmaceutical residues (carbamazepine, salicylic acid, clofibric acid, ibuprofen, 2-hydroxy-ibuprofen, fenoprofen, naproxen, ketoprofen, diclofenac, and triclosan) in sewage influent and roughly primary-treated effluent. The method involved solid-phase extraction (SPE) with polymeric sorbents, and two SPE cartridges were compared for the extraction and elution of the targeted compounds in complex matrices. A successful chemical derivatization of carbamazepine and acidic compounds using N,O-bis(trimethylsilyl) trifluoroacetamide +10% trimethylchlorosilane is also described. The quantification limits of the analytical procedure ranged from 30 to 60?ng?L^?1 for 500?mL of wastewater. The best recovery rates (72–102%) in spiked effluent samples were obtained with Phenomenex Strata-X? cartridges. Detection limits (S/N?=?3) were estimated at between 1 and 18?ng?L^?1. The reported GC–MS/MS method significantly reduces the strong matrix effects encountered with more expensive LC-MS/MS techniques. Application of the developed method showed that most selected analytes were detected at concentrations ranging from low µg?L^?1 to trace level ng?L^?1 in Montreal's wastewater treatment plant effluent and influent, as well as in the receiving waters at more than 8?km downstream of the effluent outfall. The rugged alternative analytical method is suitable for the simultaneous analysis of carbamazepine and pharmaceutical acidic residues in wastewater samples from influents and effluents that have undergone rough primary treatment.     

Square wave voltammetric determination of diafenthiuron and its application to water,soil and insecticide formulation

A square wave cathodic stripping voltammetric (SWCSV) method has been developed for the determination of insecticide diafenthiuron. The procedure is based on controlled accumulation of the insecticide on a static hanging mercury drop electrode (SHMDE) at 0.00?mV (vs. Ag/AgCl) in Britton-Robinson buffer solution (pH 7.0). The insoluble mercury compound was reduced at ?510?mV during the cathodic potential scan. The peak currents were linearly related to insecticide concentration between 30.4 and 3200?µg?L^?1 . The detection and quantification limit were 9.1?µg?L^?1 and 30.4?µg?L^?1, respectively. The proposed analytical procedure was applied to natural water and soil samples. The method was extended to direct determination of diafenthiuron in insecticide formulation Polo® 50 WP and average content of 50.3?±?1.7 (m/m) at 90% confidence level, in close agreement with the 50.0% quoted by the manufacturer. HPLC comparison method indicated that accuracy was in agreement with that obtained by the proposed method.     

Adaptive finite element solution of the porous medium equation in pressure formulation

The pressure formulation of the porous medium equation has been commonly used in theoretical studies due to its much better regularities than the original formulation. The goal here is to study its use in the adaptive moving mesh finite element solution. The free boundary is traced explicitly through Darcy's law. The method is shown numerically second‐order in space and first‐order in time in the pressure variable. Moreover, the convergence order of the error in the location of the free boundary is almost second‐order in the maximum norm. However, numerical results also show that the convergence order in the original variable stays between first‐order and second‐order in L¹ norm or between 0.5th‐order and first‐order in L² norm. Nevertheless, the current method can offer some advantages over numerical methods based on the original formulation for situations with large exponents or when a more accurate location of the free boundary is desired.     

Determination of doripenem and related substances in medicinal product using capillary electrophoresis

Doripenem, the latest carbapenem antibiotic licensed in the United States (15 October 2007) and the European Union (25 July 2008), has been implemented into therapeutic use along with imipenem, meropenem and ertapenem. The described method of zone electrophoresis in a low pH buffer for the separation of doripenem from its impurities has been successfully performed using field‐amplified sample stacking (FASS), followed by UV absorption detection at 214 nm. The best results were obtained with phosphate buffer (100 mM) pH 2.9 containing 10% (v/v) of methanol, as the background electrolyte. Uncoated fused‐silica capillary (60/52 cm; 75 μm id) with normal polarity, and voltage values of 25 kV, was used throughout the investigation. The optimised method of doripenem determination was validated in terms of linearity, accuracy and precision, and provides a detection limit of 3.0 μg/mL of doripenem. The repeatability, expressed by relative standard deviation (RSD) of the migration time, for doripenem and its degradation products varied from 1.37 to 2.51%, whereas the corrected peak areas were about 0.91–9.87%. Satisfactory separation was achieved within 20 min of electrophoresis; moreover, all carbapenems (imipenem, meropenem, ertapenem and doripenem) were well separated from each other during this time. The evaluated CZE method was applied in the analysis of a medicinal product containing doripenem Doribax^® powder for solution for infusion.     

Spectrophotometric microdetermination of anti-Parkinsonian and antiviral drug amantadine HCl in pure and in dosage forms

Two simple, rapid, sensitive, low-cost, and accurate methods (A and B) for the microdetermination of amantadine HCl (AMD) in pure form and in pharmaceutical formulations are developed. Method A is based on the formation of tris (o-phenanthroline)-iron(II) complex (ferroin) upon reaction of amantadine HCl with an iron (III)-o-phenanthroline mixture in sodium acetate-acetic acid buffer media. The ferroin complex is spectrophotometrically measured at λ_max 509 nm against reagent blank. Method B is based on the reduction of Fe (III) by the drug which forms colored complex (λ_max 521 nm) with 2,2′-bipyridyl. Optimizations of the experimental conditions are described. Beer’s law is obeyed in the concentration ranges 0.4–10 and 0.6–22 μg mL^?1 using 1,10-phenanthroline and 2,2′-bipyridyl, respectively. The developed methods have been successfully applied for the determination of AMD in bulk drugs and in pharmaceutical formulations. The common excipients and additives did not interfere in their determinations.     

Kinetic spectrophotometric determination of pravastatin in drug formulations via derivatization with 4-chloro-7-nitrobenzo-2-oxa-1,3-diazole (NBD-Cl)

A simple and sensitive kinetic spectrophotometric method for the quantitative analysis of pravastatin sodium (PVS) in pure and pharmaceutical formulations has been described. The method is based on the formation of colored product between PVS and 4-chloro-7-nitrobenzo-2-oxa-1,3-diazole (NBD-Cl) in acetone medium at 55 ± 2 °C. The reaction is followed spectrophotometrically by measuring the increase in absorbance at 462 nm as a function of time. The initial rate and fixed time methods were adopted for constructing the calibration curves. The linearity ranges were found to be 15.0–50.0 and 10.0–70.0 μg mL^?1 for initial rate and fixed time methods, respectively. The limits of detection for initial rate and fixed time methods are 0.029 and 0.086 μg mL^?1, respectively. Both methods have been applied successfully for the estimation of PVS in commercial dosage forms with no interference from the excipients. The results are compared with the HPLC pharmacopoeial method.