Quasi-Relative Interiors for Graphs of Convex Set-Valued Mappings

This paper aims at providing further studies of the notion of quasi-relative interior for convex sets introduced by Borwein and Lewis. We obtain new formulas for representing quasi-relative interiors of convex graphs of set-valued mappings and for convex epigraphs of extended-real-valued functions defined on locally convex topological vector spaces. We also show that the role, which this notion plays in infinite dimensions and the results obtained in this vein, are similar to those involving relative interior in finite-dimensional spaces.Comment: This submission replaces our previous version

THE STATUS OF PARTICIPATION IN EXTRACURRICULAR SPORT TRAINING OF STUDENTS IN SOC TRANG PROVINCE, VIETNAM

The method of sociological investigation is used in the article to survey students' opinions at colleges in Soc Trang province and provided information on the status of participation in extracurricular sports of students at colleges in Soc Trang province by gender, ethnicity and purpose.  Article visualizations

Revisiting conventional noncovalent interactions towards a complete understanding: from tetrel to pnicogen, chalcogen, and halogen bond

Typical noncovalent interactions, including tetrel (TtB), pnicogen (PniB), chalcogen (ChalB), and halogen bonds (HalB), were systematically re-investigated by modeling the N⋯Z interactions (Z = Si, P, S, Cl) between NH$_3$ – as a nucleophilic, and SiF$_4$, PF$_3$, SF$_2$, and ClF – as electrophilic components, employing highly reliable ab initio methods. The characteristics of N⋯Z interactions when Z goes from Si to Cl, were examined through their changes in stability, vibrational spectroscopy, electron density, and natural orbital analyses. The binding energies of these complexes at CCSD(T)/CBS indicate that NH$_3$ tends to hold tightly most with ClF (−34.7 kJ mol$^{−1}$) and SiF$_4$ (−23.7 kJ mol$^{−1}$) to form N⋯Cl HalB and N⋯Si TtB, respectively. Remarkably, the interaction energies obtained from various approaches imply that the strength of these noncovalent interactions follows the order: N⋯Si TtB > N⋯Cl HalB > N⋯S ChalB > N⋯P PniB, that differs the order of their corresponding complex stability. The conventional N⋯Z noncovalent interactions are characterized by the local vibrational frequencies of 351, 126, 167, and 261 cm$^{−1}$ for TtB, PniB, ChalB, and HalB, respectively. The SAPT2+(3)dMP2 calculations demonstrate that the primary force controlling their strength retains the electrostatic term. Accompanied by the stronger strength of N⋯Si TtB and N⋯Cl HalB, the AIM and NBO results state that they are partly covalent in nature with amounts of 18.57% and 27.53%, respectively. Among various analysis approaches, the force constant of the local N⋯Z stretching vibration is shown to be most accurate in describing the noncovalent interactions

Antibacterial activities of the extracts of Mimosa pudica L. an in-vitro study

Mimosa pudica L., also called sensitive plant or touch-me-not, belongs to the genus Mimosa (Family: Mimosaceae). This plant grows as a weed in nearly every parts of Vietnam and is used as a traditional medicine for the treatment of some diseases. This study aims to evaluate the antibacterial activity of the water and ethanol extracts of this plant by using disc diffusion method. The total flavonoid as quercetin equivalent (QE) per gram (dry weight) of these two extracts was also estimated. The result of tests for in-vitro antibacterial activity indicates that the ethanol extract showed significant activity against E.coli, S.aureus, B.subtilis and S.typhi with the zone of inhibition was 11mm, 19mm, 17mm and 16mm respectively. The water extract only inhibited the growth of S.aureus (14mm) and B.subtilis (15mm) and there was no resistance against E.coli and S.typhi. The analysis of total flavonoid content found that the ethanol extract contains higher amount of flavonoid than water extract and flavonoid is responsible mainly for the antibacterial activity of Mimosa pudica L

Fenchel-Rockafellar Theorem in Infinite Dimensions via Generalized Relative Interiors

In this paper we provide further studies of the Fenchel duality theory in the general frame work of locally convex topological vector (LCTV) spaces. We prove the validity of the Fenchel strong duality under some qualification conditions via generalized relative interiors imposed on the epigraphs and the domains of the functions involved. Our results directly generalize the classical Fenchel-Rockafellar theorem on strong duality from finite dimensions to LCTV spaces.Comment: arXiv admin note: text overlap with arXiv:1812.0060