Positive definite and Gram tensor complementarity problems

Given a continuous function Open image in new window and Open image in new window , the non-linear complementarity problem \(\text{ NCP }(g,q)\) is to find a vector Open image in new window such that

$$\begin{aligned} x \ge 0,~~y:=g(x) +q\ge 0~~\text{ and }~~x^Ty=0. \end{aligned}$$

We say that g has the Globally Uniquely Solvable (\(\text{ GUS }\))-property if \(\text{ NCP }(g,q)\) has a unique solution for all Open image in new window and C-property if \(\mathrm{NCP}(g,q)\) has a convex solution set for all Open image in new window . In this paper, we find a class of non-linear functions that have the \(\text{ GUS }\)-property and C-property. These functions are constructed by some special tensors which are positive semidefinite. We call these tensors as Gram tensors.

     

An Efficient One‐Pot Synthesis of 7,7‐Dimethyl‐2‐(2‐oxo‐2H‐chromen‐3‐yl)‐4‐aryl‐7,8‐dihydroquinolin‐5(6H)‐one Derivatives Using Chitosan–SO3H as Biodegradable Organocatalyst

Chitosan sulfonic acid (CS–SO₃H), a biodegradable green catalyst, was found to be an impressive system for one‐pot four‐component reaction of different aromatic aldehydes, 3‐acetylcoumarin, dimedone, and ammonium acetate leading to 7,7‐dimethyl‐2‐(2‐oxo‐2H‐chromen‐3‐yl)‐4‐aryl‐7,8‐dihydroquinolin‐5(6H)‐one under solvent‐free condition. This methodology produces diverse superiorities such as operational simplicity, short reaction time, and high yield. Further, the catalyst can be reused for four times without any noticeable decrease in the catalytic activity.     

Microwave‐Assisted Synthesis and Antituberculosis Screening of Some 4‐((3‐(Trifluoromethyl)‐5,6‐dihydro‐[1,2,4]triazolo[4,3‐a]pyrazin‐7(8H)‐l)methyl)benzenamine Hybrids

In the present investigation, a series of 4‐((3‐(trifluoromethyl)‐5,6‐dihydro‐[1,2,4]triazolo[4,3‐a]pyrazin‐7(8H)‐yl)methyl)benzenamine analogs 6a–o were synthesized and characterized by IR, NMR (¹H and ¹³C), and mass spectra. All newly synthesized compounds 6a–o were prepared under conventional and microwave irradiation methods. These compounds obtained in higher yields and in shorter reaction times in the microwave irradiation method when compared with the conventional method. Synthesized compounds 6a–o were inspected for their in vitro antitubercular activity against Mycobacterium tuberculosis H₃₇Ra using an established XTT reduction menadione assay. Among the screened compounds, 6i (IC₅₀: 1.82 μg/mL), 6j (IC₅₀: 1.02 μg/mL), and 6k (IC₅₀: 1.59 μg/mL) showed excellent activity. Furthermore, compound 6i showed MIC₉₀ value of 16.02 μg/mL. In summary, the results indicate the identification of some novel, selective, and specific inhibitors against M. tuberculosis that can be explored further for the potential antitubercular drug.     

Achiral Trisubstituted Thioureas as Secondary Ligands to CuI Catalysts: Direct Catalytic Asymmetric Addition of α‐Fluoronitriles to Imines

Thioureas have emerged as effective hydrogen‐bonding catalysts over the last two decades, and they are broadly utilized in asymmetric catalysis. We report that achiral trisubstituted thioureas function as beneficial secondary ligands to Cu^I catalysts, thereby enabling highly diastereo‐ and enantioselective addition of α‐fluoronitriles to imines. The structure of the thiourea significantly affects the reaction outcome, and kinetic experiments indicate that the thioureas enhance the stereocontrol by binding to the Cu^I complex. The reaction products can be readily transformed into valuable β‐amino acid derivatives bearing a fluorinated tetrasubstituted stereogenic center.     

Enantioselective LC–ESI–MS/MS method for quantitation of (−)-lumefantrine and (+)-lumefantrine in mice plasma and application to a pharmacokinetic study

We developed and validated a simple, sensitive, selective, and reliable LC–MS/MS–ESI method for the direct quantitation of lumefantrine (LFN) enantiomers [(−)-LFN and (+)-LFN] in mice plasma as per regulatory guideline. LFN enantiomers and carbamazepine (internal standard) were extracted from mice plasma using Strata X SPE (solid-phase extraction) cartridges. Good resolution between enantiomers was achieved on a Chiralpak IA-3 column using an isocratic mobile phase (0.1% of diethyl amine in methanol), which was delivered at a flow rate of 0.8 mL/min. Detection and quantitation were performed using multiple reaction monitoring mode following the transitions m/z 530.27 → 512.30 and 237.00 → 194.00 for LFN enantiomers and the internal standard, respectively, in the positive-ionization mode. The proposed method provided accurate and reproducible results over the linearity range of 2.39–895 ng/mL for each enantiomer. The intra- and inter-day precisions were in the range of 1.03–6.14 and 6.36–8.70 and 2.03–4.88 and 5.82–11.5 for (−)-LFN and (+)-LFN, respectively. Both (−)-LFN and (+)-LFN were found to be stable under different stability conditions. The method was successfully used to delineate stereoselective pharmacokinetics of LFN enantiomers in mice after an oral administration of rac-LFN (20 mg/kg). The pharmacokinetic results indicated that the disposition of LFN enantiomers was stereoselective in mice.     

Transition-metal free synthesis of diaryl vinyl selenides: a simple synthetic approach with high selectivity

A simple, highly efficient synthetic protocol is developed for the synthesis of unsymmetrical diaryl vinyl selenides from diaryldiselenide and β-bromo styrene under transition-metal free conditions in N,N′-dimethyl propylene urea and 130 °C to afford high yields and excellent selectivities. This method provides a new strategy to fabricate a wide variety of important substituted molecular skeletons and an alternative to conventionally used metal salts, additives, and ligands.     

Coconut shell particles reinforced cardanol–formaldehyde resole resin biocomposites: Effect of treatment on thermal properties

The current work focuses on the thermal behavior of biocomposites based on cardanol formaldehyde resin (CFR) reinforced with untreated and treated coconut shell particles (CSP). CFR has been synthesized by condensing cardanol with formaldehyde in the presence of NH₄OH catalyst (ratio of 1:1.6:0.36). Fabricating biocomposites is performed by compression moulding technique. The CSP with particle size of 50?µm is used in various proportions: 30 and 40?wt%. The CSP is immersed in 5?wt% NaOH solution for 5?h. Fourier transform infrared spectroscopy is used to characterize chemical formation of the new biocomposites. Thermogravimetric analysis and differential thermal analysis are applied to measure the thermal stability of composites. The thermal stability exhibits a slight decrease with particles loading from 30 to 40?wt% against neat CFR. This work gives a path for the possibility of CSP usage in low-value products in composite manufacturing.     

Characterization of symmetric and asymmetric lipid bilayers composed of varying concentrations of ganglioside GM1 and DPPC

Gangliosides are a group of structurally diverse, sialic acid containing glycosphingolipids embedded into the membrane via their hydrophobic ceramide moiety. To gain atomic level insights into the structural perturbations caused by Galbeta3GalNAcbeta4(NeuAcalpha3)Galbeta4Glc1Cer (GM1), molecular dynamics (MD) simulations of a 1,2-dipalmitoyl-sn-glycero-3-phosphatidylcholine (DPPC) bilayer containing GM1 at five different concentrations have been performed. Biological membranes contain GM1 only on the exoplasmic leaflet. However, vesicles prepared in the laboratory contain GM1 in both the leaflets albeit unequally. Hence, simulations were performed with GM1 present in only one (asymmetric bilayers) or in both of the leaflets (symmetric bilayers) of the bilayer. In symmetric bilayers, there is a decrease in surface area, an increase in deuterium order parameter, and an increase in peak-to-peak distance of DPPC with increasing concentration of GM1. Thus, the overall area of the lipid bilayer decreases (condensation effect) and the thickness increases with increasing concentrations of GM1. Even in asymmetric systems, decrease in surface area and increase in deuterium order parameter of hydrocarbon chains of DPPC are observed. However, the decrease in bilayer area and the increase in bilayer thickness are not as much as in the symmetric bilayer.