The Inhibitory Effects of Plant Derivate Polyphenols on the Main Protease of SARS Coronavirus 2 and Their Structure–Activity Relationship

The main protease (M^pro) is a major protease having an important role in viral replication of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), the novel coronavirus that caused the pandemic of 2020. Here, active M^pro was obtained as a 34.5 kDa protein by overexpression in E. coli BL21 (DE3). The optimal pH and temperature of M^pro were 7.5 and 37 °C, respectively. M^pro displayed a K_m value of 16 μM with Dabcyl-KTSAVLQ↓SGFRKME-Edans. Black garlic extract and 49 polyphenols were studied for their inhibitory effects on purified M^pro. The IC₅₀ values were 137 μg/mL for black garlic extract and 9–197 μM for 15 polyphenols. The mixtures of tannic acid with puerarin, daidzein, and/or myricetin enhanced the inhibitory effects on M^pro. The structure–activity relationship of these polyphenols revealed that the hydroxyl group in C3′, C4′, C5′ in the B-ring, C3 in the C-ring, C7 in A-ring, the double bond between C2 and C3 in the C-ring, and glycosylation at C8 in the A-ring contributed to inhibitory effects of flavonoids on M^pro.     

Local regularity criteria of a suitable weak solution to MHD equations

We present a regularity condition of a suitable weak solution to the MHD equations in three dimensional space with slip boundary conditions for a velocity and magnetic vector fields. More precisely, we prove a suitable weak solution are H¨older continuous near boundary provided that the scaled mixed L_(x,t)~(p,q) -norm of the velocity vector field with 3/p + 2/q ≤ 2,2 q ∞ is sufficiently small near the boundary. Also, we will investigate that for this solution u ∈ L_(x,t)~(p,q) with 1≤3/p+2/q≤3/2, 3 p ∞, the Hausdorff dimension of its singular set is no greater than max{p, q}(3/p+2/q-1).     

Au nanolenses for near-field focusing

We report a novel strategy for the synthesis of Pt@Au nanorings possessing near-field focusing capabilities at the center through which single-particle surface enhanced Raman scattering could be readily observed. We utilized Pt@Au nanorings as a light-absorber; the absorbed light could be focused at the center with the aid of a Au nanoporous structure. We synthesized the Au nanolens structure through a Galvanic exchange process between Au ions and Ag block at the inner domain of the Pt@Au nanoring. For this step, Ag was selectively pre-deposited at the inner domain of the Pt@Au nanorings through electrochemical potential-tuned growth control and different surface energies with regard to the inner and outer boundaries of the nanoring. Then, the central nanoporous architecture was fabricated through the Galvanic exchange of sacrificial Ag with Au ions leading to the resulting Au nanoring with a Au nanoporous structure at the center. We monitored the shape-transformation by observing their corresponding localized surface plasmon resonance (LSPR) profiles. By varying the rim thickness of the starting Pt@Au nanorings, the inner diameter of the nanolens was accordingly tuned to maximize near-field focusing, which enabled us to obtain the reproducible and light-polarization independent measurements of single-particle SERS. Through theoretical simulation, the near-field electromagnetic field focusing capability was visualized and confirmed through single-particle SERS measurement showing an enhancement factor of 1.9 × 10⁸ to 1.0 × 10⁹.

We synthesized a Au nanolens with electromagnetic near-field focusing capability by integrating a Au nanoporous structure at the center of the Pt@Au nanoring via synthetic steps of eccentric growth of Ag and nanoscale Galvanic exchange reaction.     

Some regularity criteria of a weak solution to the 3D Navier–Stokes equations in a domain

Archiv der Mathematik - We give some regularity criterion (of a weak $$-L^{p}$$ Serrin type) of a weak solution to the 3D Navier–Stokes equations in a bounded domain $$\Omega \subset \mathbb...     

Interior Condition on Suitable Weak Solutions to the 3D MHD Equations Via Pressure

We present an interior regularity condition for suitable weak solutions with respect to the magnetic pressure under the class of scaling invariance.     

Infinitely many solutions for polyharmonic equations of p(x)-Laplace type

We show the existence of infinitely many weak solutions to a class of quasilinear elliptic p(x)-polyharmonic Kirchhoff equations via the mountain pass principle without the (AR) condition. Furthermore, we obtain infinitely many solutions to this equation based on the genus theory, introduced by Krasnoselskii and the abstract critical point theorem (a variant of Ljusternik-Schnirelman theory) under Cerami condition.     

Elliptic problems involving the p-Laplacian in ℝN with locally Lipschitz functional

We study the existence of infinitely many weak solutions for the elliptic type equation via a general nonsmooth critical point theorem.