Distribution dependent stochastic differential equations

Due to their intrinsic link with nonlinear Fokker-Planck equations and many other applications, distribution dependent stochastic differential equations (DDSDEs) have been intensively investigated. In this paper, we summarize some recent progresses in the study of DDSDEs, which include the correspondence of weak solutions and nonlinear Fokker-Planck equations, the well-posedness, regularity estimates, exponential ergodicity, long time large deviations, and comparison theorems.     

On the Relative Twist Formula of l-adic Sheaves

We propose a conjecture on the relative twist formula of l-adic sheaves, which can be viewed as a generalization of Kato—Saito's conjecture. We verify this conjecture under some transversal assumptions. We also define a relative cohomological characteristic class and prove that its formation is compatible with proper push-forward. A conjectural relation is also given between the relative twist formula and the relative cohomological characteristic class.     

基于不确定控制理论的最优策略研究

本文在不确定理论的框架下,研究一类带背景状态变量的最优控制模型.在乐观值准则下,利用不确定动态规划的方法,证明了不确定最优性原则,得到最优性方程.作为应用,求解一个固定缴费(DC)型养老金的最优投资策略问题,在乐观值准则下,以工资变量为背景状态变量,建立养老金模型.通过求解不确定最优性方程得到最优投资策略和最优支付率.     

Fast Cysteine Bioconjugation Chemistry

Cysteine bioconjugation serves as a powerful tool in biological research and has been widely used for chemical modification of proteins, constructing antibody-drug conjugates, and enabling cell imaging studies. Cysteine conjugation reactions with fast kinetics and exquisite selectivity have been under heavy pursuit as they would allow clean protein modification with just stoichiometric amounts of reagents, which minimizes side reactions, simplifies purification and broadens functional group tolerance. In this concept, we summarize the recent advances in fast cysteine bioconjugation, and discuss the mechanism and chemical principles that underlie the high efficiencies of the newly developed cysteine reactive reagents.     

基于流量测点的热网变动阻力系数优化辨识

随着供热计量系统的普及，系统可以根据负荷的变化进行调整，管网的阻力系数随即发生变化。对变动阻力系数进行优化辨识是了解供热管网实时运行状况的有效手段。提出一种基于流量监测数据的供热管网变动阻力系数优化辨识方法，并利用遗传算法进行求解。对洛阳市某小区供暖季管网实际运行数据进行验证，辨识结果的相对误差在5%以内。结果表明：该方法可以在只有流量观测数据时得到精度较高的供热管网变动阻力系数，为供热系统的运行调节提供指导。     

Decay rate for viscoelastic wave equation of variable coefficients with delay and dynamic boundary conditions

In this paper, we consider a viscoelastic wave equation of variable coefficients in the presence of past history with nonlinear damping and delay in the internal feedback and dynamic boundary conditions. Under suitable assumptions, we establish an explicit and general decay rate result without imposing restrictive assumption on the behavior of the relaxation function at infinity by Riemannian geometry method and Lyapunov functional method.     

Addendum to “On the Riesz potential operator of variable order from variable exponent Morrey space to variable exponent Campanato space”, Math Meth Appl Sci. 2020; 1–8

In the paper mentioned in the title, it is proved the boundedness of the Riesz potential operator of variable order α(x) from variable exponent Morrey space to variable exponent Campanato space, under certain assumptions on the variable exponents p(x) and λ(x) of the Morrey space. Assumptions on the exponents were different depending on whether $\frac{\alpha (x)p(x)?n+\lambda (x)}{p(x)}$ takes or not the critical values 0 or 1. In this note, we improve those results by unifying all the cases and covering the whole range $0?\frac{\alpha (x)p(x)?n+\lambda (x)}{p(x)}?1$. We also provide a correction to some minor technicality in the proof of Theorem 2 in the aforementioned paper.