Positive solutions of Schr\"odinger equations and fine regularity of boundary points

Given a Lipschitz domain $\Omega$ in ${\mathbb R} ^N$ and a nonnegative potential $V$ in $\Omega$ such that $V(x)\, d(x,\partial \Omega)^2$ is bounded in $\Omega$ we study the fine regularity of boundary points with respect to the Schr\"odinger operator $L_V:= \Delta -V$ in $\Omega$. Using potential theoretic methods, several conditions equivalent to the fine regularity of $z \in \partial \Omega$ are established. The main result is a simple (explicit if $\Omega$ is smooth) necessary and sufficient condition involving the size of $V$ for $z$ to be finely regular. An essential intermediate result consists in a majorization of $\int_A | {\frac {u} {d(.,\partial \Omega)}} | ^2\, dx$ for $u$ positive harmonic in $\Omega$ and $A \subset \Omega$. Conditions for almost everywhere regularity in a subset $A$ of $\partial \Omega$ are also given as well as an extension of the main results to a notion of fine ${\mathcal L}_1 | {\mathcal L}_0$-regularity, if ${\mathcal L}_j={\mathcal L}-V_j$, $V_0,\, V_1$ being two potentials, with $V_0 \leq V_1$ and ${\mathcal L}$ a second order elliptic operator.Comment: version 1. 23 pages version 3. 28 pages. Mainly a typo in Theorem 1.1 is correcte

Binding mode analyses and pharmacophore model development for stilbene derivatives as a novel and competitive class of α-glucosidase inhibitors

Stilbene urea derivatives as a novel and competitive class of non-glycosidic α-glucosidase inhibitors are effective for the treatment of type II diabetes and obesity. The main purposes of our molecular modeling study are to explore the most suitable binding poses of stilbene derivatives with analyzing the binding affinity differences and finally to develop a pharmacophore model which would represents critical features responsible for α-glucosidase inhibitory activity. Three-dimensional structure of S. cerevisiae α-glucosidase was built by homology modeling method and the structure was used for the molecular docking study to find out the initial binding mode of compound 12, which is the most highly active one. The initial structure was subjected to molecular dynamics (MD) simulations for protein structure adjustment at compound 12-bound state. Based on the adjusted conformation, the more reasonable binding modes of the stilbene urea derivatives were obtained from molecular docking and MD simulations. The binding mode of the derivatives was validated by correlation analysis between experimental Ki value and interaction energy. Our results revealed that the binding modes of the potent inhibitors were engaged with important hydrogen bond, hydrophobic, and π-interactions. With the validated compound 12-bound structure obtained from combining approach of docking and MD simulation, a proper four featured pharmacophore model was generated. It was also validated by comparison of fit values with the Ki values. Thus, these results will be helpful for understanding the relationship between binding mode and bioactivity and for designing better inhibitors from stilbene derivatives

Ab initio investigations of the electronic and magnetic structures of CoH and CoH2

First principles investigation of the structural, electronic and magnetic properties study of cobalt and the hydrides CoHx (x = 1, 2) show significant volume expansion effect versus Co-H bonding. As hydrogen is incorporated in the cobalt lattice, the density of states undergoes gradual modifications within the valence band and particularly near the Fermi level. A resulting strong reduction of magnetization characterizes the dihydride whereas the monohydride is revealed as a strong ferromagnet, like Co

Immunomodulatory Therapy for MIS-C

CONTEXT: Studies comparing initial therapy for multisystem inflammatory syndrome in children (MIS-C) provided conflicting results.OBJECTIVE: To compare outcomes in MIS-C patients treated with intravenous immunoglobulin (IVIG), glucocorticoids, or the combination thereof. DATA SOURCES: Medline, Embase, CENTRAL and WOS, from January 2020 to February 2022. STUDY SELECTION: Randomized or observational comparative studies including MIS-C patients <21 years. DATA EXTRACTION: Two reviewers independently selected studies and obtained individual participant data. The main outcome was cardiovascular dysfunction (CD), defined as left ventricular ejection fraction < 55% or vasopressor requirement ≥ day 2 of initial therapy, analyzed with a propensity score-matched analysis. RESULTS: Of 2635 studies identified, 3 nonrandomized cohorts were included. The meta-analysis included 958 children. IVIG plus glucocorticoids group as compared with IVIG alone had improved CD (odds ratio [OR] 0.62 [0.42–0.91]). Glucocorticoids alone group as compared with IVIG alone did not have improved CD (OR 0.57 [0.31–1.05]). Glucocorticoids alone group as compared with IVIG plus glucocorticoids did not have improved CD (OR 0.67 [0.24–1.86]). Secondary analyses found better outcomes associated with IVIG plus glucocorticoids compared with glucocorticoids alone (fever ≥ day 2, need for secondary therapies) and better outcomes associated with glucocorticoids alone compared with IVIG alone (left ventricular ejection fraction < 55% ≥ day 2). LIMITATIONS: Nonrandomized nature of included studies. CONCLUSIONS: In a meta-analysis of MIS-C patients, IVIG plus glucocorticoids was associated with improved CD compared with IVIG alone. Glucocorticoids alone was not associated with improved CD compared with IVIG alone or IVIG plus glucocorticoids