Optimal control of the obstacle problem: optimality conditions

^** E-mail: k.aithadi{at}ucam.ac.ma In this paper, we investigate optimal control problem governedby variational inequality of the obstacle type. Existence ofsolution for the problem is proved and we also show how to obtainoptimality conditions for a penalized problem issued from theoriginal one.     

Effect of Concentrated Salts Solutions on the Stability of Immobilized Enzymes: Influence of Inactivation Conditions and Immobilization Protocol

This paper aims to investigate the effects of some salts (NaCl, (NH₄)₂SO₄ and Na₂SO₄) at pH 5.0, 7.0 and 9.0 on the stability of 13 different immobilized enzymes: five lipases, three proteases, two glycosidases, and one laccase, penicillin G acylase and catalase. The enzymes were immobilized to prevent their aggregation. Lipases were immobilized via interfacial activation on octyl agarose or on glutaraldehyde-amino agarose beads, proteases on glyoxyl agarose or glutaraldehyde-amino agarose beads. The use of high concentrations of salts usually has some effects on enzyme stability, but the intensity and nature of these effects depends on the inactivation pH, nature and concentration of the salt, enzyme and immobilization protocol. The same salt can be a stabilizing or a destabilizing agent for a specific enzyme depending on its concentration, inactivation pH and immobilization protocol. Using lipases, (NH₄)₂SO₄ generally permits the highest stabilities (although this is not a universal rule), but using the other enzymes this salt is in many instances a destabilizing agent. At pH 9.0, it is more likely to find a salt destabilizing effect than at pH 7.0. Results confirm the difficulty of foreseeing the effect of high concentrations of salts in a specific immobilized enzyme.     

One pot diastereoselective synthesis of new chiral spiro‐1,3,4‐thiadiazoles and 1,4,2‐oxathiazoles from (1R)‐thiocamphor

Herein we report an efficient one pot synthesis of new chiral 4,5‐dihydro‐4‐arylspiro[1,3,4‐thiadiazole]‐5,2′‐camphane‐2‐carboxylic acid ethyl esters 5–7 and 4,5‐dihydro‐3‐arylspiro[1,4,2‐oxathiazole]‐5,2′‐camphane 11–13 , using 1,3‐dipolar cycloaddition of nitrilimines 2–4 and nitrile oxides 8–10 to (1R)‐thiocamphor 1 respectively. The structure of the newly prepared 1,3,4‐thiadiazoles 5–7 (obtained as pure diastereoisomers) were fully established via spectroscopic analysis and X‐ray structural analysis which proved the absolute configuration of the C5 spiranic carbon to be (R). NMR spectral analysis were also very useful to show the new 1,4,2‐oxathiazoles 11–13 are mixtures of two (5R)/(5S) diastereoisomers with the ratio 6:4,7:3 and 6:4 respectively.     

Organocatalytic asymmetric syntheses of functionalized tetrahydropyridazines

Four tetrahydropyridazines, respectively, substituted at the C-3 position with hydroxymethyl, a silyloxymethyl, a carboxylic acid, and a methyl ester have been prepared in good yields and high enantiomeric purities using organocatalytic α-amination of aldehydes as the key step. These compounds have then been tested as organocatalysts for the same reaction.     

An approach to the interpretation of backpropagation neural network models in QSAR studies

An approach to the interpretation of backpropagation neural network models for quantitative structure-activity and structure-property relationships (QSAR/QSPR) studies is proposed. The method is based on analyzing the first and second moments of distribution of the values of the first and the second partial derivatives of neural network outputs with respect to inputs calculated at data points. The use of such statistics makes it possible not only to obtain actually the same characteristics as for the case of traditional "interpretable" statistical methods, such as the linear regression analysis, but also to reveal important additional information regarding the non-linear character of QSAR/QSPR relationships. The approach is illustrated by an example of interpreting a backpropagation neural network model for predicting position of the long-wave absorption band of cyane dyes.     

Rare Sugars: Recent Advances and Their Potential Role in Sustainable Crop Protection

Rare sugars are monosaccharides with a limited availability in the nature and almost unknown biological functions. The use of industrial enzymatic and microbial processes greatly reduced their production costs, making research on these molecules more accessible. Since then, the number of studies on their medical/clinical applications grew and rare sugars emerged as potential candidates to replace conventional sugars in human nutrition thanks to their beneficial health effects. More recently, the potential use of rare sugars in agriculture was also highlighted. However, overviews and critical evaluations on this topic are missing. This review aims to provide the current knowledge about the effects of rare sugars on the organisms of the farming ecosystem, with an emphasis on their mode of action and practical use as an innovative tool for sustainable agriculture. Some rare sugars can impact the plant growth and immune responses by affecting metabolic homeostasis and the hormonal signaling pathways. These properties could be used for the development of new herbicides, plant growth regulators and resistance inducers. Other rare sugars also showed antinutritional properties on some phytopathogens and biocidal activity against some plant pests, highlighting their promising potential for the development of new sustainable pesticides. Their low risk for human health also makes them safe and ecofriendly alternatives to agrochemicals.     

Hybrid of the 1,2,3-triazole nucleus and sesquiterpene skeleton as a potential antitumor agent: Hemisynthesis,molecular structure,Hirshfeld surface analysis,density functional theory,and in vitro cytotoxic and apoptotic effects

A new 1,2,3-triazole sesquiterpenic named (4aR,5aS,7aR,10aR,10bR)-10-benzyl-5,5-dichloro-1,1,4a,7a-tetramethyl-1,2,3,4,4a,5,7a,10,10a,10b decahydrocyclopropa[2′,3′]cyclohepta [1′,2′:3,4]benzo[1,2-d][1,2,3]triazol-7(6H)-one was synthesized by a dipolar cycloaddition 1,3 between benzyl azide and α,β-unsaturated sesquiterpene ketone catalyzed by titanium tetrachloride TiCl₄. It was obtained with a good yield and characterized using single-crystal X-ray diffraction technique, infra red (IR) spectroscopy, High Resolution Mass Spectrometry (HRMS), UV-Visible, and ¹H and ¹³C NMR spectroscopies. The optimization by the density functional theory (DFT) method was carried out to study the formation mechanism of the derivative. The selected compounds 1 – 4 exhibited anticancer activities in vitro against namely fibrosarcoma (HT-1080), lung carcinoma (A-549), and breast (MCF-7 and MDA-MB-231 cell lines with IC₅₀ in the range of 10.02–44.71 μM). In addition to using flow cytometry and the apoptosis assay, cell cycle arrest at the S phase (10 μM) and G2/M arrest in (5 and 10 μM) was performed for compound 4 in fibrosarcoma (HT-1080) cancer cells. Results suggested that compound 4 test with good activity against HT-1080 cells with IC₅₀ value from 10.02 μM and induced the apoptotic effect. Theoretical studies were realized to estimate the molecular proprieties that lead to a high potential of cytotoxic effect, which is in agreement with the experimental results.     

Assessment of Corrosion Inhibition Performance and Adsorption Thermodynamics of Hydrogen Phosphate (HPO42−) and Molybdate (MoO42−) Oxyanions on Tin in Maleic Acid

The influence of hydrogen phosphate (HPO₄²⁻) and molybdate ions (MoO₄²⁻) on the behavior of tin corrosion in 0.2 M maleic acid was compared using experimental and theoretical techniques. The experimental studies consisted of the electrochemical investigations (potentiodynamic polarization (PDP) and electrochemical impedance spectroscopy (EIS)), along with the surface analytical techniques (SEM and EDX). Additionally, the theoretical analysis (the chemical quantum computations at MP4/SDD level of theory in the aqueous phase), was conducted. The experimental outcomes illustrated that the inhibition efficiency (η%) increases with the concentration of the inhibitors, reaching 88 % and 81 % at 2×10⁻² M concentration of MoO₄²⁻ and HPO₄²⁻, respectively. The potentiodynamic polarization curves revealed that HPO₄²⁻ performance is a cathodic-type inhibitor, while MoO₄²⁻ shows a mixed-type behavior. The increase in temperature decreased the η% values of both inhibitors. Based on surface analysis and thermodynamic study, the presence of the two inhibitors formed protective films on the tin surface through a physisorption mechanism. The chemical quantum computations using the complete fourth-order Møller Plesset perturbation theory (MP4 with SDD basis) method results outlined the favorable affinity of the investigated inorganic inhibitors to interact with the tin surface, which interprets the well-observed inhibition efficiencies.     

Mathematical modeling of respiratory viral infection and applications to SARS-CoV-2 progression

Viral infection in cell culture and tissue is modeled with delay reaction-diffusion equations. It is shown that progression of viral infection can be characterized by the viral replication number, time-dependent viral load, and the speed of infection spreading. These three characteristics are determined through the original model parameters including the rates of cell infection and of virus production in the infected cells. The clinical manifestations of viral infection, depending on tissue damage, correlate with the speed of infection spreading, while the infectivity of a respiratory infection depends on the viral load in the upper respiratory tract. Parameter determination from the experiments on Delta and Omicron variants allows the estimation of the infection spreading speed and viral load. Different variants of the SARS-CoV-2 infection are compared confirming that Omicron is more infectious and has less severe symptoms than Delta variant. Within the same variant, spreading speed (symptoms) correlates with viral load allowing prognosis of disease progression.