Biharmonic PNMC Submanifolds in Spheres

We obtain several rigidity results for biharmonic submanifolds in $\mathbb{S}^{n}$ with parallel normalized mean curvature vector field. We classify biharmonic submanifolds in $\mathbb{S}^{n}$ with parallel normalized mean curvature vector field and with at most two distinct principal curvatures. In particular, we determine all biharmonic surfaces with parallel normalized mean curvature vector field in $\mathbb{S}^n$. Then we investigate, for (not necessarily compact) proper biharmonic submanifolds in $\mathbb{S}^n$, their type in the sense of B-Y. Chen. We prove: (i) a proper biharmonic submanifold in $\mathbb{S}^n$ is of 1-type or 2-type if and only if it has constant mean curvature {\mcf}=1 or {\mcf}\in(0,1), respectively; (ii) there are no proper biharmonic 3-type submanifolds with parallel normalized mean curvature vector field in $\mathbb{S}^n$.Comment: 17 page

Unraveling the performance of dispersion-corrected functionals for the accurate description of weakly bound natural polyphenols

Long-range non-covalent interactions play a key role in the chemistry of natural polyphenols. We have previously proposed a description of supramolecular polyphenol complexes by the B3P86 density functional coupled with some corrections for dispersion. We couple here the B3P86 functional with the D3 correction for dispersion, assessing systematically the accuracy of the new B3P86-D3 model using for that the well-known S66, HB23, NCCE31, and S12L datasets for non-covalent interactions. Furthermore, the association energies of these complexes were carefully compared to those obtained by other dispersion-corrected functionals, such as B(3)LYP-D3, BP86-D3 or B3P86-NL. Finally, this set of models were also applied to a database composed of seven non-covalent polyphenol complexes of the most interest.FDM acknowledges financial support from the Swedish Research Council (Grant No. 621-2014-4646) and SNIC (Swedish National Infrastructure for Computing) for providing computer resources. The work in Limoges (IB and PT) is supported by the “Conseil Régional du Limousin”. PT gratefully acknowledges the support by the Operational Program Research and Development Fund (project CZ.1.05/2.1.00/03.0058 of the Ministry of Education, Youth and Sports of the Czech Republic). IB gratefully acknowledges financial support from “Association Djerbienne en France”

Synthesis and Biological Screening of New 4-Hydroxycoumarin Derivatives and Their Palladium(II) Complexes

Two newly synthesized 4-hydroxycoumarin bidentate ligands (L1 and L2) and their palladium(II) complexes (C1 and C2) were screened for their biological activities, in vitro and in vivo. Structures of new compounds were established based on elemental analysis, 1H NMR, 13C NMR, and IR spectroscopic techniques. The obtained compounds were tested for their antioxidative and cytotoxic activities and results pointed to selective antiradical activity of palladium(II) complexes towards •OH and -•OOH radicals and anti-ABTS (2,2′-Azino-bis(3-ethylbenzothiazoline-6-sulfonic acid) cation radical) activity comparable to that of ascorbate. Results indicated the effect of C1 and C2 on the enzymatic activity of the antioxidative defense system. In vitro cytotoxicity assay performed on different carcinoma cell lines (HCT166, A375, and MIA PaCa-2), and one healthy fibroblast cell line (MRC-5) showed a cytotoxic effect of both C1 and C2, expressed as a decrease in carcinoma cells' viability, mostly by induction of apoptosis. In vivo toxicity tests performed on zebrafish embryos indicated different effects of C1 and C2, ranging from adverse developmental effect to no toxicity, depending on tested concentration. According to docking studies, both complexes (C1 and C2) showed better inhibitory activity in comparison to other palladium(II) complexes