光触发自修复聚合物研究进展

近几年,由于光触发自修复聚合物具有可控快速等优势,其在自修复聚合物领域中占据了重要的地位。光触发自修复聚合物实现自修复的方法主要分为3类,分别是基于光交联反应的自修复、基于光触发交换反应的自修复和基于光热效应的自修复。本文主要从光触发自修复聚合物的修复机制以及修复过程中涉及的化学本质两个方面,重点阐述了上述3类光触发自修复方法的最新研究进展,强调3种光触发自修复之间的联系和共同点。同时,对光触发自修复聚合物未来的发展前景进行了展望。     

The p-th moment stability of solutions to impulsive stochastic differential equations driven by G-Brownian motion

In this paper, we consider a class of impulsive stochastic differential equations driven by G-Brownian motion (IGSDEs in short). By means of the G-Lyapunov function method, some criteria on p-th moment stability and p-th moment asymptotical stability for the trivial solutions of IGSDEs are established. An example is presented to illustrate the efficiency of the obtained results.     

Equality of the homogeneous and the Gabor wave front set

We prove that Hörmander’s global wave front set and Nakamura’s homogeneous wave front set of a tempered distribution coincide. In addition, we construct a tempered distribution with a given wave front set, and we develop a pseudodifferential calculus adapted to Nakamura’s homogeneous wave front set.     

Law of Large Numbers for Branching Symmetric Hunt Processes with Measure-Valued Branching Rates

We establish weak and strong laws of large numbers for a class of branching symmetric Hunt processes with the branching rate being a smooth measure with respect to the underlying Hunt process, and the branching mechanism being general and state dependent. Our work is motivated by recent work on the strong law of large numbers for branching symmetric Markov processes by Chen and Shiozawa (J Funct Anal 250:374–399, 2007) and for branching diffusions by Engländer et al. (Ann Inst Henri Poincaré Probab Stat 46:279–298, 2010). Our results can be applied to some interesting examples that are covered by neither of these papers.     

Existence of multiplicity harmonic and subharmonic solutions for second‐order quasilinear equation via Poincaré‐Birkhoff twist theorem

In this paper, we investigate the existence and multiplicity of harmonic and subharmonic solutions for second‐order quasilinear equation where , g satisfies the superlinear condition at infinity. We prove that the given equation possesses harmonic and subharmonic solutions by using the phase‐plane analysis methods and a generalized version of the Poincaré‐Birkhoff twist theorem.     

近切触流形的φ*-解析向量场

本文引入了近切触流形（M,ø,ξ,η,g）中φ^*-解析向量场的概念,并研究了其性质.利用近切触流形的性质,证明了切触度量流形中的φ^*-解析向量场v是Killing向量场且φv不是φ^*-解析的.特别地,如果近切触流形M是正规的,得到v与ξ平行且模长为常数.另外,证明了3维的切触度量流形不存在非零的φ^*-解析向量场.     

Infinitely many non-radial solutions for fractional Nirenberg problem

In this paper, the prescribed \(\sigma \)-curvature problem

$$\begin{aligned} P_{\sigma }^{g_0} u={\tilde{K}}(x)u^{\frac{N+2\sigma }{N-2\sigma }}, x\in {\mathbb {S}}^N,u>0 \end{aligned}$$

is considered. When \({\tilde{K}}(x)\) is some axis symmetric function on \({\mathbb {S}}^N\), by using singular perturbation method, it is proved that this problem possesses infinitely many non-radial solutions for \(0<\sigma \le 1\) and \(N> 2\sigma +2\).

     

Modified classification of non-self-adjoint second-order difference equations

This paper is concerned with the classification of non-self-adjoint second-order difference equations. The relationship between the number of summable solutions of non-self-adjoint difference equations and that of the discrete linear Hamiltonian system is discussed. A classification for non-self-adjoint second-order difference equations is established, which is independent of the choice of the rotated half plane and the fixed point.     

Rigidity Theorems for Complete Sasakian Manifolds with Constant Pseudo-Hermitian Scalar Curvature

The orthogonal decomposition of the Webster curvature provides us a way to characterize some canonical metrics on a pseudo-Hermitian manifold. We derive some subelliptic differential inequalities from the Weitzenböck formulas for the traceless pseudo-Hermitian Ricci tensor of Sasakian manifolds with constant pseudo-Hermitian scalar curvature and the Chern–Moser tensor of the Sasakian pseudo-Einstein manifolds, respectively. By means of either subelliptic estimates or maximum principle, some rigidity theorems are established to characterize Sasakian pseudo-Einstein manifolds among Sasakian manifolds with constant pseudo-Hermitian scalar curvature and Sasakian space forms among Sasakian pseudo-Einstein manifolds, respectively.     

Designing Solid Electrolyte Interfaces towards Homogeneous Na Deposition: Theoretical Guidelines for Electrolyte Additives and Superior High-Rate Cycling Stability

Metallic Na is a promising metal anode for large-scale energy storage. Nevertheless, unstable solid electrolyte interphase (SEI) and uncontrollable Na dendrite growth lead to disastrous short circuit and poor cycle life. Through phase field and ab initio molecular dynamics simulation, we first predict that the sodium bromide (NaBr) with the lowest Na ion diffusion energy barrier among sodium halogen compounds (NaX, X=F, Cl, Br, I) is the ideal SEI composition to induce the spherical Na deposition for suppressing dendrite growth. Then, 1,2-dibromobenzene (1,2-DBB) additive is introduced into the common fluoroethylene carbonate-based carbonate electrolyte (the corresponding SEI has high mechanical stability) to construct a desirable NaBr-rich stable SEI layer. When the Na||Na₃V₂(PO₄)₃ cell utilizes the electrolyte with 1,2-DBB additive, an extraordinary capacity retention of 94 % is achieved after 2000 cycles at a high rate of 10 C. This study provides a design philosophy for dendrite-free Na metal anode and can be expanded to other metal anodes.