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.     

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.     

光化学的初级过程和次级过程

针对物理化学教材中有关光化学初级过程和次级过程、初级过程的量子产率、初级过程的反应速率表示以及是否是零级反应等问题发表了看法。