The martingale problem for a class of nonlocal operators of diagonal type

We consider systems of stochastic differential equations of the form $$\begin{array}{c}\hfill d{X}_t^i=\sum _{j=1}^d{A}_{ij}\left(X_{t?}\right)d{Z}_t^j\end{array}$$ for $i=1,?,d$ with continuous, bounded and non‐degenerate coefficients. Here $Z_t^1,?,Z_t^d$ are independent one‐dimensional stable processes with ${\alpha }_1,?,{\alpha }_d\in (0,2)$. In this article we research on uniqueness of weak solutions to such systems by studying the corresponding martingale problem. We prove the uniqueness of weak solutions in the case of diagonal coefficient matrices.     

Singular Hamiltonian elliptic systems with critical exponential growth in dimension two

We will focus on the existence of nontrivial solutions to the following Hamiltonian elliptic system where are numbers belonging to the interval [0, 2), V is a continuous potential bounded below on by a positive constant and the functions f and g possess exponential growth range established by Trudinger–Moser inequalities in Lorentz–Sobolev spaces. The proof involves linking theorem and a finite‐dimensional approximation.     

Weighted estimates for the multilinear maximal function on the upper half‐spaces

For a general dyadic grid, we give a Calderón–Zygmund type decomposition, which is the principle fact about the multilinear maximal function on the upper half‐spaces. Using the decomposition, we study the boundedness of . We obtain a natural extension to the multilinear setting of Muckenhoupt's weak‐type characterization. We also partially obtain characterizations of Muckenhoupt's strong‐type inequalities with one weight. Assuming the reverse Hölder's condition, we get a multilinear analogue of Sawyer's two weight theorem. Moreover, we also get Hytönen–Pérez type weighted estimates.     

增材制造金属反射镜的发展综述

随着光学测量与遥感领域的不断发展,折反式光学系统对重量、体积和环境适应性等需求不断提高。基于增材制造技术的金属反射镜以其便于实现优化设计、快速制造和加工工艺性好等优点,逐渐获得国内外学者的关注与研究。与传统金属反射镜相比,增材制造金属反射镜可以提高反射镜的结构刚度,同时可实现更高程度的轻量化。增材制造反射镜可以满足光学系统对环境适应性和快速性的需求。本文首先讨论了金属反射镜的评价指标;其次,综述了国内外在基于增材制造技术制备金属反射镜领域的发展现状和技术参数,从增材制造金属反射镜的基体设计与制备和基体的后处理2个方面展开论述;然后,通过分析,总结了增材制造金属反射镜的技术路线和关键技术;最后,对增材制造反射镜的应用前景提出了展望。     

A Multiresponsive Functional AIEgen for Spatiotemporal Pattern Control and All-round Information Encryption

Functional materials with multi-responsive properties and good controllability are highly desired for developing bioinspired and intelligent multifunctional systems. Although some chromic molecules have been developed, it is still challenging to realize in situ multicolor fluorescence changes based on a single luminogen. Herein, we reported an aggregation-induced emission (AIE) luminogen called CPVCM, which can undergo a specific amination with primary amines to trigger luminescence change and photoarrangement under UV irradiation at the same active site. Detailed mechanistic insights were carried out to illustrate the reactivity and reaction pathways. Accordingly, multiple-colored images, a quick response code with dynamic colors, and an all-round information encryption system were demonstrated to show the properties of multiple controls and responses. It is believed that this work not only provides a strategy to develop multiresponsive luminogens but also develops an information encryption system based on luminescent materials.