Integral Representations of the Large and Little Schröder Numbers

In the paper, the authors establish several integral representations for the generating functions of the large and little Schröder numbers and for the large and little Schröder numbers.     

Mesoscopic Modeling of Capillarity-Induced Two-Phase Transport in a Microfluidic Porous Structure

Mesoscopic modeling at the pore scale offers great promise in exploring the underlying structure transport performance of flow through porous media. The present work studies the fluid flow subjected to capillarity-induced resonance in porous media characterized by different porous structure and wettability. The effects of porosity and wettability on the displacement behavior of the fluid flow through porous media are discussed. The results are presented in the form of temporal evolution of percentage saturation and displacement of the fluid front through porous media. The present study reveals that the vibration in the form of acoustic excitation could be significant in the mobilization of fluid through the porous media. The dependence of displacement of the fluid on physicochemical parameters like wettability of the surface, frequency along with the porosity is analyzed. It was observed that the mean displacement of the fluid is more in the case of invading fluid with wetting phase where the driving force strength is not so dominant.     

Three-term polynomial progressions in subsets of finite fields

We prove that the group of diffeomorphisms of the interval [0, 1] contains surface groups whose action on (0, 1) has no global fix point and such that only countably many points of the interval (0, 1) have non-trivial stabiliser.     

Chemical Profiles and Pharmacological Properties with in Silico Studies on Elatostema papillosum Wedd

The current study attempted, for the first time, to qualitatively and quantitatively determine the phytochemical components of Elatostema papillosum methanol extract and their biological activities. The present study represents an effort to correlate our previously reported biological activities with a computational study, including molecular docking, and ADME/T (absorption, distribution, metabolism, and excretion/toxicity) analyses, to identify the phytochemicals that are potentially responsible for the antioxidant, antidepressant, anxiolytic, analgesic, and anti-inflammatory activities of this plant. In the gas chromatography-mass spectroscopy analysis, a total of 24 compounds were identified, seven of which were documented as being bioactive based on their binding affinities. These seven were subjected to molecular docking studies that were correlated with the pharmacological outcomes. Additionally, the ADME/T properties of these compounds were evaluated to determine their drug-like properties and toxicity levels. The seven selected, isolated compounds displayed favorable binding affinities to potassium channels, human serotonin receptor, cyclooxygenase-1 (COX-1), COX-2, nuclear factor (NF)-κB, and human peroxiredoxin 5 receptor proteins. Phytol acetate, and terpene compounds identified in E. papillosum displayed strong predictive binding affinities towards the human serotonin receptor. Furthermore, 3-trifluoroacetoxypentadecane showed a significant binding affinity for the KcsA potassium channel. Eicosanal showed the highest predicted binding affinity towards the human peroxiredoxin 5 receptor. All of these findings support the observed in vivo antidepressant and anxiolytic effects and the in vitro antioxidant effects observed for this extract. The identified compounds from E. papillosum showed the lowest binding affinities towards COX-1, COX-2, and NF-κB receptors, which indicated the inconsequential impacts of this extract against the activities of these three proteins. Overall, E. papillosum appears to be bioactive and could represent a potential source for the development of alternative medicines; however, further analytical experiments remain necessary.     

NMR spectral analysis of strongly second-order 6-, 8-, 9- and 10- spin-systems (1H─19F, 19F─19F,and 13C─19F) in perfluorotoluyl- and tetrafluoro-pyridyl-aromatics using the lineshape method ANATOLIA

A simple to use nuclear magnetic resonance analysis method has been tested on complex ¹H, ¹⁹F, and ¹³C multiplets. This open-source line-shape analysis method analysis of total lineshape (ANATOLIA)¹ provides some significant advantages over traditional assign-iterate methods of NMR spectral analysis by avoiding false minima and progressing optimisation to the global minimum. The target molecules are 1-perfluorotol-4-yl-2-perfluorotol-4-yl-oxymethyl-1H-benzimidazole (molecule-I) and 1-tetrafluoropyrid-4-yl-2-tetrafluoropyrid-4-yl-thio-1H-benzimidazole (molecule-II) which were produced as part of a family of fluorinated drug scaffolds prepared for anticancer and antiparasitic screening. Spectra display significant second-order effects with ¹H Δδ = 3.68 and 4.67 Hz for the aromatic hydrogen “triplets”, with ¹⁹F ⁴J_AA', ⁴J_BB', ⁴J_XX', and ⁴J_YY' coupling constants range from +4.8 to −14.0 Hz and for ¹³C-isotopomers ¹⁹F Δδ of up to 111.56 Hz. A spin-system of six coupling nuclei (H_aH_bH_cH_d F_YF_Y') was analysed in 12 s, a spin-system of nine coupling fluorine nuclei (AA'BB'CCC-YY') was analysed within 2 min, and 10 coupling nuclei (XX'YY'ZZZ-BB'-H_d) was optimised in 6 min using a laptop computer. ANATOLIA was also robust enough to be able to yield accurate spectral values from inaccurate input values. In both compounds, a fluorine–fluorine coupling constant was identified between the two fluoro-aromatic rings (F_BB' and F_YY') of +4.05 and +4.67 Hz and attributed to a through-space interaction. Ab initio structure optimisations and coupling constant calculations provided useful input data for spectral analysis. A modern ¹⁹F nuclear magnetic resonance spectrum of perfluorotoluene (octafluorotoluene) and analysis from 1975 was used as a test data set to assess ANATOLIA.