Off-diagonal Aubry-André (AA) model has recently attracted a great deal of attention as they provide condensed matter realization of topological phases. We numerically study a generalized off-diagonal AA model with p-wave superfluid pairing in the presence of both commensurate and incommensurate hopping modulations. The phase diagram as functions of the modulation strength of incommensurate hopping and the strength of the p-wave pairing is obtained by using the multifractal analysis. We show that with the appearance of the p-wave pairing, the system exhibits mobility-edge phases and critical phases with various number of topologically protected zero-energy modes. Predicted topological nature of these exotic phases can be realized in a cold atomic system of incommensurate bichromatic optical lattice with induced p-wave superfluid pairing by using a Raman laser in proximity to a molecular Bose-Einstein condensation.

In this paper, we introduce the notion of weak θ-φ-contraction ensuring a convergence of successive approximations but does not force the mapping to be continuous at the fixed point. Thus, we answer one more solution to the open question raised

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Paederia scandens (Lour.) Merr. (P. scandens), as an edible and medicinal herb, is commonly used for treating gastric ulcer in China; however, its mechanistic and effective substances’ studies remain limited. This study aimed to investigate the antigastric ulcer effects of aqueous extracts of P. scandens (PS-AE) and explore the involvement of NF-κB signaling in this effect. In addition, the study aimed to identify the effective substances by exploring NF-κB inhibitors. The main components of PS-AE were identified using an UPLC-MS method. HCl/EtOH-induced acute gastric ulcer in rats, and LPS-stimulated RAW264.7 cells were used to determine the antigastric ulcer effects of PS-AE in vivo and in vitro, respectively. Histopathological changes of the ulcer tissues were observed using staining methods of HE and PAS; secretions of inflammatory cytokines and oxidative stress indexes were measured using biochemical test kits; protein levels of NF-κB signaling pathway-related molecules were measured using Western Blot. NF-κB inhibitors’ identification in P. scandens was performed by developing HipHop pharmacophore model, and the results were further validated by molecular docking. In vivo, PS-AE significantly attenuated gastric ulcer in rats; reduced inflammation by adjusting the inflammatory cytokines TNF-α, IL-1β, and IL-6 levels; and induced oxidative stress can be alleviated via adjusting the levels of SOD, MDA, and GSH-Px. In addition, PS-AE may play an anti-inflammatory role mainly through NF-κB signaling pathway. Following pharmacophore modeling and molecular docking, 13 potential inhibitors targeting NF-κB were identified. In addition, in vitro, PS-AE and paederoside could significantly inhibit the activation of NF-κB p65 and the productions of downstream cytokines including NO, TNF-α, and IL-6. PS-AE protective effects on gastric ulcer damage induced by HCl/EtOH in rats, which is probably associated with its antioxidant effect and the inhibitory effects on levels of inflammatory mediators regulated by NF-κB signaling pathway. 13 potential NF-κB-targeting inhibitors are probably effective substances contributing to the herb’s pharmacological effect. In practical application, Paederia scandens, a traditional food and medicinal plant, possessed diversified chemical components and multiple pharmacological activities (anti-inflammatory, bacteriostasis, and antioxidative.). In China, P. scandens has been used as a traditional medicine to treat gastritis for hundreds of years, and it may be a potentially effective dietary product to improve gastric ulcer. This study shows that P. scandens exerts protective effects on gastric ulcer damage induced by HCl/EtOH in rats, which is probably associated with its antioxidant effect and the inhibitory effects on levels of inflammatory mediators regulated by NF-κB signaling pathway, which provides pharmacological justifications for the functional food use of P. scandens for treating gastric disease.

We provide a diagrammatic approach to compute the algebraic structures on the Grothendieck group of a tower of the Temperley–Lieb algebras.