On the Existence of Solutions for the Critical Fractional Laplacian Equation in ℝ

We study existence of solutions for the fractional Laplacian equation -Δsu+Vxu=u2*s-2u+fx, u in ℝN, u∈Hs(RN), with critical exponent 2*s=2N/(N-2s), N>2s, s∈0, 1, where Vx≥0 has a potential well and f:ℝN×ℝ→ℝ is a lower order perturbation of the critical power u2*s-2u. By employing the variational method, we prove the existence of nontrivial solutions for the equation

Chiral Plasmons with Twisted Atomic Bilayers

van der Waals heterostructures of atomically thin layers with rotational misalignments, such as twisted bilayer graphene, feature interesting structural moir ' e superlattices. Because of the quantum coupling between the twisted atomic layers, light-matter interaction is inherently chiral; as such, they provide a promising platform for chiral plasmons in the extreme nanoscale. However, while the interlayer quantum coupling can be significant, its influence on chiral plasmons still remains elusive. Here we present the general solutions from full Maxwell equations of chiral plasmons in twisted atomic bilayers, with the consideration of interlayer quantum coupling. We find twisted atomic bilayers have a direct correspondence to the chiral metasurface, which simultaneously possesses chiral and magnetic surface conductivities, besides the common electric surface conductivity. In other words, the interlayer quantum coupling in twisted van der Waals heterostructures may facilitate the construction of various (e.g., bi-anisotropic) atomically-thin metasurfaces. Moreover, the chiral surface conductivity, determined by the interlayer quantum coupling, determines the existence of chiral plasmons and leads to a unique phase relationship (i.e., +/-pi/2 phase difference) between their transverse-electric (TE) and transverse-magnetic (TM) wave components. Importantly, such a unique phase relationship for chiral plasmons can be exploited to construct the missing longitudinal spin of plasmons, besides the common transverse spin of plasmons

In Vitro Glucuronidation of Wushanicaritin by Liver Microsomes, Intestine Microsomes and Expressed Human UDP-Glucuronosyltransferase Enzymes

Wushanicaritin, a natural polyphenol compound, exerts many biological activities. This study aimed to characterize wushanicaritin glucuronidation by pooled human liver microsomes (HLM), human intestine microsomes and individual uridine diphosphate-glucuronosyltransferase (UGT) enzyme. Glucuronidation rates were determined by incubating wushanicaritin with uridine diphosphoglucuronic acid-supplemented microsomes. Kinetic parameters were derived by appropriate model fitting. Reaction phenotyping, the relative activity factor (RAF) and activity correlation analysis were performed to identify the main UGT isoforms. Wushanicaritin glucuronidation in HLM was efficient with a high CLint (intrinsic clearance) value of 1.25 and 0.69 mL/min/mg for G1 and G2, respectively. UGT1A1 and 1A7 showed the highest activities with the intrinsic clearance (CLint) values of 1.16 and 0.38 mL/min/mg for G1 and G2, respectively. In addition, G1 was significantly correlated with β-estradiol glucuronidation (r = 0.847; p = 0.0005), while G2 was also correlated with chenodeoxycholic acid glucuronidation (r = 0.638, p = 0.026) in a bank of individual HLMs (n = 12). Based on the RAF approach, UGT1A1 contributed 51.2% for G1, and UGT1A3 contributed 26.0% for G2 in HLM. Moreover, glucuronidation of wushanicaritin by liver microsomes showed marked species difference. Taken together, UGT1A1, 1A3, 1A7, 1A8, 1A9 and 2B7 were identified as the main UGT contributors responsible for wushanicaritin glucuronidation