Existence of positive solutions of (p(x),q(x))-Laplacian parabolic systems with right hand side defined as a multiplication of two separate functions

The paper deals with the study of the existence of weak positive solutions for a new class of the system of parabolic differential equations with respect to the symmetry conditions by using sub-super solutions method. Our results are natural extensions from our previous ones in (Bol. Soc. Mat. Mex. 2019; 25:145-162) and (Appl. Math E-Notes. 2018; 18:209-218), where we have already studied the existence of positive solutions for some classes of Laplacian elliptic problems by using one classical method.     

Recovery of acetaminophen from aqueous solutions using a supported liquid membrane based on a quaternary ammonium salt as ionophore

A flat sheet-supported liquid membrane (FSSLM) system, consisting of an ionic liquid, tricapryl-methylammonium chloride (Aliquat 336®) in octan-2-ol, is proposed as a means of recovering acetaminophen (Ac) from aqueous solutions; Ac is an active ingredient widely used in many pharmaceutical preparations. Several parameters which could affect the transport efficiency were examined, i.e., the strippant nature and concentration in the receiving solution, the diluent nature, carrier concentration, initial acetaminophen concentration in the feed solution, and the polymeric support type. A facilitated transport was obtained by impregnating the polymeric support with 10 vol. % of Aliquat 336® in octan-2-ol, 1 M NaOH as a receiving solution, and a feed solution of Ac dissolved in ultrapure water. The study was completed by using the FSSLM thus developed for extracting Ac from some drugs in frequent use in Tunisia (Analgan®, Doliprane®, and Fervex®).     

Analysis of Menger’s ‘spatiotemporal hypothesis’

Ab initio at HF/6-31G and HF/6-31G(d,p) levels, AM1 and molecular mechanics calculations of thermodynamic and kinetic parameters for Menger’s system 1-3 (an important enzyme model) indicate that the remarkable enhancement in the proton transfer process is largely the result of a strain effect, and this strain is a function of the bond distance between the two reacting centers and the value of the angle of attack.     

Computationally-designed phenylephrine prodrugs – a model for enhancing bioavailability

DFT calculations at B3LYP 6-31G (d,p) for intramolecular proton transfer in a number of Kirby's enzyme models demonstrated that the driving force for the proton transfer efficiency is the distance between the two reactive centres (r_GM) and the attack angle (α); and the rate of the reaction is linearly correlated with r_GM² and sin (180°- α). Based on these results three phenylephrine prodrugs were designed to provide phenylephrine with higher bioavailability than their parent drug. Using the experimental t_1/2 (the time needed for the conversion of 50% of the reactants to products) and EM (effective molarity) values for these processes the t_1/2 values for the conversion of the three prodrugs to the parent drug, phenylephrine were calculated. The calculated t_1/2 values for ProD 1 and ProD 2 were very high (145 days and several years, respectively) whereas that of ProD 3 was found to be about 35 hours. Therefore, the intra-conversion rates of the phenylephrine prodrugs to phenylephrine can be programmed according to the nature of the prodrug linker.     

Proximity vs. strain in intramolecular ring-closing reactions

The DFT and ab initio calculation results for ring-closing reactions of eight different ω-bromoalkanecarboxylate anions (1–8) reveal that the activation energy (ΔG ^?) for the intramolecular cyclization process is strongly correlated with both (i) the experimental intramolecular cyclization rate (log k _intra) and (ii) the distance between the two reactive centres, whereas the slope values of the change in enthalpy (ΔH) vs. the attack angle (α) and the distance between the two reacting centres (r) were found to correlate strongly with the experimental strain energy of the cycle being formed (E _{s Exp}). These results assist in designing pro-prodrug systems that can be utilized to improve the overall biopharmaceutical profile of current medications in order to enhance their effectiveness and ease their utility.     

Analyzing Kirby’s amine olefin—a model for amino acid ammonia lyases

Ab initio and DFT calculations on the ring-closing reaction of Kirby’s amine olefin (ammonia lyase enzyme model) reveal that the process involves two consecutive steps: proton transfer from a molecule of water to the carbon-carbon double bond followed by nucleophilic attack of the amine nitrogen onto the second carbon of the double bond. Further, they indicate that the second step in the process is barrier less due to the combination of the release in strain energy upon conversion of the reactant to the product and, the proximity orientation of the nucleophile to the electrophile. Effective molarity (EM) calculations establish that Kirby’s amine olefin process undergoes ring-closing at a rate that is comparable to the rates of reactions catalyzed by the most efficient enzymes.