Some properties of Hermite-based Sheffer polynomials

In this paper, the concepts and the formalism associated with monomiality principle and Sheffer sequences are used to introduce family of Hermite-based Sheffer polynomials. Some properties of Hermite-Sheffer polynomials are considered. Further, an operational formalism providing a correspondence between Sheffer and Hermite-Sheffer polynomials is developed. Furthermore, this correspondence is used to derive several new identities and results for members of Hermite-Sheffer family.     

Hermite-based Appell polynomials: Properties and applications

By employing certain operational methods, the authors introduce Hermite-based Appell polynomials. Some properties of Hermite-Appell polynomials are considered, which proved to be useful for the derivation of identities involving these polynomials. The possibility of extending this technique to introduce Hermite-based Sheffer polynomials (for example, Hermite-Laguerre and Hermite-Sister Celine's polynomials) is also investigated.     

Selective and sensitive determination of peptides using 3,4-dihydroxyphenylacetic acid as a fluorogenic reagent

A novel fluorescence (FL) reaction for N-terminal Gly-containing peptides has been developed using 3,4-dihydroxyphenylacetic acid (3,4-DHPAA). The reaction of the peptides with 3,4-DHPAA was carried out in borate buffer (pH 8.0) in the presence of sodium periodate at 37 °C for 10 min, and the FL was measured with a spectrofluorimeter at the excitation and emission wavelengths of 370 nm and 465 nm, respectively. The 3,4-DHPAA reagent generated particularly strong FL for peptides containing Gly at their N-termini. When various other bio-substances, such as amino acids, sugars, nucleic bases, nucleotides, and proteins, were reacted with 3,4-DHPAA, no FL was observed. Under optimized reaction conditions, the lower detection limit of 0.25 μmol L⁻¹ was obtained for the N-terminal Gly-containing peptides of Gly-Pro (GP) and Gly-Pro-Pro (GPP), which gave 3 times greater FL intensity than that observed for the reagent blank. The proposed reaction with 3,4-DHPAA as a fluorogenic reagent is selective and sensitive for the detection of N-terminal Gly-containing peptides, and therefore, this method could be a useful tool for the determination of these particular oligopeptides.     

Self-phase modulation signatures of neuronal activity

We use phase-sensitive detection of spectral hole refilling to demonstrate strong novel intrinsic nonlinear signatures of neuronal activation in hippocampal brain slices. The ability to gain access to this fundamentally new intrinsic contrast with modest power levels suggests a new approach to in vivo neural imaging. We expect that we can extrapolate our method to high spatial and temporal resolution in deep tissue while retaining the noninvasive character.     

Stereocontrolled access to isoprostanes via a bicyclo[3.3.0]octene framework

We report a simple and highly stereocontrolled strategy toward the total synthesis of isoprostanes based on a bicyclic alpha,beta-epoxy ketone intermediate 6. Bicyclo[3.3.0]octene scaffold permitted stereodirection of reagents allowing stereoselective epoxidation, diastereoselective ketone reduction, and regioselective epoxide opening otherwise not accessible with a simple cyclopentene framework.     

Perturbed and non-perturbed Brownian taboo processes

In this paper we study the Brownian taboo process, which is a version of Brownian motion conditioned to stay within a finite interval, and the α-perturbed Brownian taboo process, which is an analogous version of an α-perturbed Brownian motion.We are particularly interested in the asymptotic behaviour of the supremum of the taboo process, and our main results give integral tests for upper and lower functions of the supremum as t→∞. In the Brownian case these include extensions of recent results in Lambert [4], but are proved in a quite different way.     

Synthesis,Antimicrobial, Anticancer,PASS, Molecular Docking,Molecular Dynamic Simulations & Pharmacokinetic Predictions of Some Methyl β-D-Galactopyranoside Analogs

A series of methyl β-D-galactopyranoside (MGP, 1) analogs were selectively acylated with cinnamoyl chloride in anhydrous N,N-dimethylformamide/triethylamine to yield 6-O-substitution products, which was subsequently converted into 2,3,4-tri-O-acyl analogs with different acyl halides. Analysis of the physicochemical, elemental, and spectroscopic data of these analogs revealed their chemical structures. In vitro antimicrobial testing against five bacteria and two fungi and the prediction of activity spectra for substances (PASS) showed promising antifungal functionality comparing to their antibacterial activities. Minimum inhibition concentration (MIC) and minimum bactericidal concentration (MBC) tests were conducted for four compounds (4, 5, 6, and 9) based on their activity. MTT assay showed low antiproliferative activity of compound 9 against Ehrlich’s ascites carcinoma (EAC) cells with an IC₅₀ value of 2961.06 µg/mL. Density functional theory (DFT) was used to calculate the thermodynamic and physicochemical properties whereas molecular docking identified potential inhibitors of the SARS-CoV-2 main protease (6Y84). A 150-ns molecular dynamics simulation study revealed the stable conformation and binding patterns in a stimulating environment. In-silico ADMET study suggested all the designed molecules to be non-carcinogenic, with low aquatic and non-aquatic toxicity. In summary, all these antimicrobial, anticancer and in silico studies revealed that newly synthesized MGP analogs possess promising antiviral activity, to serve as a therapeutic target for COVID-19.