A soft version of the Knaster–Tarski fixed point theorem with applications

In this paper, first, we define a partial order on a soft set (F, A) and introduce some related concepts. Then, using the concept of a soft mapping introduced by Babitha and Sunil (Comput Math Appl 60(7):1840–1849, 2010), a soft version of Knaster–Tarski fixed point theorem is obtained. Some examples are presented to support the concepts introduced and the results proved herein. As an application of our result, we show that the soft Knaster–Tarski fixed point theorem ensures the existence of a soft common fixed point for a commuting family of order-preserving soft mappings.     

MgFe<Subscript>2</Subscript>O<Subscript>4</Subscript>/cellulose/SO<Subscript>3</Subscript>H nanocomposite: a new biopolymer-based nanocatalyst for one-pot multicomponent syntheses of polysubstituted tetrahydropyridines and dihydropyrimidinones

A new biopolymer cellulose-based magnetic heterogeneous catalyst, MgFe₂O₄/cellulose/SO₃H nanocomposite, was prepared. Fourier-transform infrared spectra, X-ray diffraction, energy-dispersive X-ray, field-emission scanning electron microscopy, thermal analysis (TG, DTG and DSC), dynamic light scattering and vibrating sample magnetometer measurements have been used to characterize the catalyst. Then, it was applied efficiently as an inexpensive and green catalyst in two multicomponent syntheses of polysubstituted tetrahydropyridines and dihydropyrimidinones under solvent-free conditions. The nanocatalyst can be recovered and reused several times without significant loss of catalytic activity.     

Photoluminescence investigation of MPA–ZnS QDs interaction with selenite ion

The interaction between water-soluble zinc sulfide quantum dots (ZnS QDs) and selenite ion was investigated by photoluminescence method. The water-soluble ZnS QDs were synthesized using a simple and fast procedure based on the co-precipitation of nanoparticles in an aqueous solution in the presence of 3-mercaptopropionic acid (MPA), as the capping agent. Fluorescence intensity for MPA–ZnS QDs, with a strong fluorescent emission at about 430 nm, decreased in the presence of selenite. The influence of the effective parameters including pH and temperature was investigated. The results showed that under the optimum conditions, the fluorescence intensity change of QDs was linearly proportional to the selenite concentration in the range 4.0 × 10^?5–7.2 × 10^?4 mol L^?1. Moreover, the quenching mechanism was discussed to be a static quenching procedure.     

Progress in the Application of Nanoparticles and Graphene as Drug Carriers and on the Diagnosis of Brain Infections

The blood–brain barrier (BBB) is the protective sheath around the brain that protects the sensitive microenvironments of the brain. However, certain pathogens, viruses, and bacteria disrupt the endothelial barrier and cause infection and hence inflammation in meninges. Macromolecular therapeutics are unable to cross the tight junctions, thereby limiting their bioavailability in the brain. Recently, nanotechnology has brought a revolution in the field of drug delivery in brain infections. The nanostructures have high targeting accuracy and specificity to the receptors in the case of active targeting, which have made them the ideal cargoes to permeate across the BBB. In addition, nanomaterials with biomimetic functions have been introduced to efficiently cross the BBB to be engulfed by the pathogens. This review focuses on the nanotechnology-based drug delivery approaches for exploration in brain infections, including meningitis. Viruses, bacteria, fungi, or, rarely, protozoa or parasites may be the cause of brain infections. Moreover, inflammation of the meninges, called meningitis, is presently diagnosed using laboratory and imaging tests. Despite attempts to improve diagnostic instruments for brain infections and meningitis, due to its complicated and multidimensional nature and lack of successful diagnosis, meningitis appears almost untreatable. Potential for overcoming the difficulties and limitations related to conventional diagnostics has been shown by nanoparticles (NPs). Nanomedicine now offers new methods and perspectives to improve our knowledge of meningitis and can potentially give meningitis patients new hope. Here, we review traditional diagnosis tools and key nanoparticles (Au-NPs, graphene, carbon nanotubes (CNTs), QDs, etc.) for early diagnosis of brain infections and meningitis.     

Enhancement of the biochemical activity of some market antibiotics by chemical modification: Synthesis,characterization, and biochemical evaluation

The reaction of isatin with the Ampicillin gave the new compound: (6R)‐3,3‐dimethyl‐7‐oxo‐6‐(2‐(([E]‐2‐oxoindolin‐3‐ylidene)amino)‐2‐phenylacetamido)‐4‐thia‐1‐azabicyclo[3.2.0]hept ‐ane‐2‐carboxylic acid (HAI). The new complexes derived from HAI and Co(II), Ni(II), Cu(II), Eu(III), and Gd(III) were obtained in pure form. The obtained compounds were characterized by elemental analysis, FTIR, UV–Vis, Fluorescence, ¹HNMR, Mass spectra, DTA, TGA, Magnetic susceptibility, X‐ray, AAS, and the conductivity of 0.001 M in DMSO. The obtained data indicated the formation of the target complexes: [Co(HAI)(H₂O)(NO₃)]NO₃.4H₂O, [Ni(AI)(H₂O)₂]Cl.2H₂O, [Cu(AI)]Cl.H₂O, [Eu(AI)(H₂O)Cl]Cl.5H₂O and [Gd(AI)(H₂O)(NO₃)]NO₃.3H₂O. The ligation sites were predicted from the guide of the FTIR and thermal analysis meanwhile the stereochemistry was proved by the UV–Vis and magnetic moment. Co(II) and Ni(II) gave an octahedral structure while Cu(II) gave a square planar form. Molecular modeling, molecular mechanics, and DFT calculations were carried out for the synthesized compounds. The active lone pair and surface properties were obtained and discussed in the silico level. The x‐ray analysis indicates the nanoparticle behavior of the Cu‐AI complex with a monoclinic structure. The interactions of the synthesized complexes with FM‐DNA moiety were investigated through spectrometric titration (UV–vis. spectra) and by using fluorescence spectroscopy. The modes and binding affinities were evaluated and discussed using Benesi–Hildebrand method. Antimicrobial activities of the synthesized compounds have been screened using the disc diffusion method. HAI and Cu‐AI gave activity exceeded the Ampicillin. The docking work was carried using the targeting protein of Escherichia coli FabH (PDB code: 1HNJ). The obtained binding energy was compared and discussed in terms of the in vitro studies.     

Sonosynthesis of spiroindolines using functionalized SBA-15

Functionalized SBA-15 (immobilization of Pd on the modified SBA-15) has been used as an efficient catalyst for the preparation of spiroindolines by multi-component reactions of isatins, cyclic-1,3-diketones, and 6-amino-1,3-dimethyluracil under ultrasonic irradiation in water. The catalyst has been characterized by X-ray diffraction spectroscopy (XRD), field emission scanning electron microscopy (FE-SEM), transmission electron microscopy (TEM), energy-dispersive X-ray spectroscopy (EDX), X-ray photoelectron spectroscopy (XPS), Fourier transform infrared spectroscopy (FT-IR), N₂ adsorption analysis, temperature-programmed desorption (TPD), and thermogravimetric analysis (TGA). The advantages of this method include the reusability of the catalyst, low catalyst loading, excellent yields in short reaction times and easy separation of products, and use of ultrasonic irradiation as a valuable and powerful technology.

     

Relativistic polytropic models of charged anisotropic compact objects

In this paper, we introduce new viable solutions to the Einstein-Maxwell field equations by incorporating the features of anisotropic matter distributions within the realm of the general theory of relativity (\begin{document}${\rm GR}$\end{document}). To obtain these solutions, we employed the Finch-Skea spacetime, along with a generalized polytropic equation of state (\begin{document}${\rm EoS}$\end{document}). We constructed various models of generalized polytropes by assuming different values of the polytropic index, i.e., \begin{document}$\eta= \dfrac{1}{2},~ \dfrac{2}{3},~ 1$\end{document}, and \begin{document}$ 2 $\end{document}. Next, numerous physical characteristics of these considered models were studied via graphical analysis, and they were found to obey all the essential conditions for astrophysical compact objects. Furthermore, such outcomes of charged anisotropic compact star models could be reproduced in various other cases including linear, quadratic, and polytropic \begin{document}${\rm EoS}$\end{document}     

One-Pot Synthesis of Benzo[4,5]imidazo[1,2-a]pyrimidin-2-ones Using a Hybrid Catalyst Supported on Magnetic Nanoparticles in Green Solvents

The conversion of soluble polyoxometalate into insoluble polyoxometalate is considered to be one of the major challenges in synthetic organic chemistry. Here, polyoxometalate was bonded to the salt part of an organic branch immobilized on the silica-coated Fe₃O₄ nanoparticle and characterized using various techniques. The fabricated complex was used as a heterogeneous catalyst in a novel one-pot reaction for synthesis of benzo[4,5]imidazo[1,2-a]pyrimidin-2-ones using aromatic amines, dimethyl acetylenedicarboxylate (DMAD), derivatives of benzaldehyde and 2-aminobenzimidazole in water/ethanol as a green solvent. 21 derivatives of benzo[4,5]imidazo[1,2-a]pyrimidin-2-one were synthesized by this method and fully characterized. The high stability of the catalyst showed that it can be reused for 6 times without decreasing in activity. The combination of new synthetic method, new ferromagnetic heterogeneous nano-catalyst, green solvent and simple separation method were presented in this work.     

Graphene quantum dot–based electrochemical biosensing for early cancer detection

Electrochemical biosensing systems coupled with graphene quantum dots (GQDs) have demonstrated suitability for cancer diagnostic strategies, particularly to identify the changes facilitating the early phases of tumorigenesis as well as to detect ultralow concentrations of biomarkers that distinguish between normal and malignant cells. GQDs, known as a novel class of zero-dimensional semiconductor nanocrystals, are tiny graphene particles arranged in a honeycomb structure with a size range of 1–50 nm. The size of these GQDs is comparable with the size of biomolecules, thereby providing an ideal platform to study biomolecules such as proteins, cells, and viruses. GQDs are a superior platform for specific and sensitive recognition of cancer biomarkers; they are highly synergistic with electrochemical sensors. This review will shed light on the recent advancements made in the field of GQD-based electrochemical sensors for early cancer detection, with the aim of highlighting the prospects for further development in cancer diagnostics.     

Synthesis and Cytotoxic Activity of Some Novel Dihyrobenzo[h]pyrano[3,2‐c]chromene Derivatives

Three‐component reaction of 4‐hydroxy‐2H‐benzo[h]chromen‐2‐one, aromatic aldehydes, and malononitrile in the presence of 1,4‐diazabicyclo[2.2.2]octane (DABCO) in ethanol at room temperature affords good yields of novel dihyrobenzo[h]pyrano[3,2‐c]chromene derivatives. The synthesized compounds examined by MTT assays for cytotoxic activity in two human cancer cell lines (MOLT‐4, HL‐60). Most of the evaluated compounds showed low inhibitory activity against tumor cell line at micromolar concentrations.