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In this paper we study the lattice quasi-periodic operators with power-law long-range hopping and meromorphic monotone potentials, and diagonalize the operators via a Nash-Moser iteration scheme. As applications, we obtain uniform power-law localization, uniform dynamical localization and Lipschitz continuity of the integrated density of states (IDS) for such operators. Our main motivation comes from investigating quantum suppression of chaos in a quantum kicked rotor model with non-analytical potential. [ABSTRACT FROM AUTHOR]

In this paper we give a multi-scale analysis proof of the power-law localization for random operators on Z d for arbitrary d ≥ 1. [ABSTRACT FROM AUTHOR]

In this paper, we consider the nonlinear elliptic equations on rectangular tori. Using methods in the study of KAM theory and Anderson localization, we prove that these equations admit many analytic solutions. [ABSTRACT FROM AUTHOR]

In this paper, it is proved that the full dimensional invariant tori obtained by Bourgain [J. Funct. Anal., 229 (2005), no. 1, 62–94] is stable in a very long time for 1D nonlinear Schrödinger equation with periodic boundary conditions. [ABSTRACT FROM AUTHOR]

In this paper, we study the long-time stability of solutions for the 1-dimensional nonlinear Schrödinger equation (NLS) on the torus. Precisely, we prove the super-exponential long time stability of solutions with initial data in some modified Sobolev space. This generalizes the exponential long time stability result of Biasco-Massetti-Procesi ([2020, CMP]). The main new ingredient here lies on the key observation of some tame type inequality. [ABSTRACT FROM AUTHOR]

MiR-155 is reported as immune regulated miRNA in mammalian corresponding to immunity, antibacterial and antiviral effects regulation. However, the roles and mechanisms of the miRNA have remained largely undefined. We herein comprehensively investigated the functions of miR-155 in vitro and in vivo by miR-155 mimics, agomir and antagomir in Cyprinus carpio and Ictalurus punctatus , with the target genes in the SOSC1 pathway certified in I. punctatus via luciferase reporter assays. Results showed that the miR-155 regulated the expressions of cytokines, including TNF-α, IFN-γ, IL-1β, IL-6 and IL-10. Further research confirmed SOSC1 as one of the targets of the miRNA, and the JAK1/STAT3/SOSC1 signal pathway involved in the miR-155 effects on the expression of immune cytokines as well. Additionally, the changes of TLR2 in fish may also be related to miR-155 along with its target SOCS1, and the TLR2/MyD88 pathway may partly participate in the effects of the miR-155 on the cytokines. The research here confirmed that the miR-155 can regulate cytokines expression by SOSC1 signal pathways of fish in vitro and in vivo, which would provide resources for understanding and studying about immune regulation in fish. • Firstly investigated the immune functions of miR-155 of fish in vitro and in vivo. • Proved the miR-155 regulating immune cytokines expressions in different fishes. • Certified the SOSC1 as the target of miR-155 by Luciferase reporter assay. • Certified JAK1/STAT3/SOSC1 pathway being involved in the miR-155 immune effects. • Certified TLR2/MyD88 pathway being correlated to the immune effects of miR-155. [ABSTRACT FROM AUTHOR]