Autonomous linear neutral equations with bounded Borel functions as initial data

Various Non-autonomous Notions for Borel Measures

We introduce and investigate the notions of expansiveness, topological stability and persistence for Borel measures with respect to time varying bi-measurable maps on metric spaces. We prove that expansive persistent measures are topologically stable in the class of all time varying homeomorphisms.

带非自治线性D算子的中立型泛函微分方程的指数阶

Exponential Ordering for Neutral Functional Differential Equations With Non-Autonomous Linear D-Operator

该研究针对带稳定线性非自治$D$-算子的中立型泛函微分方程，证明卷积算子$\u001b[D\tilde]$的可逆性与一致连续性，引入新的变换指数阶并推导极小集1-覆盖性质，最终将结论应用于一类房室系统的物质量描述。

非自治迭代函数系统的拓扑压力变分原理

A Variational Principle for the Topological Pressure of Non-autonomous Iterated Function Systems on Subsets

本文提出非自治迭代函数系统的Pesin-Pitskel拓扑压力定义，并建立其与测度论压力的变分原理。

基于预解算子技术的二阶脉冲中立型微分方程的可控性

Controllability of a second-order impulsive neutral differential equation via resolvent operator technique

本文利用预解算子技术研究Banach空间中二阶非自治中立型脉冲积微分方程的温和解存在性与近似可控性，并借助半群理论、图范数和Krasnoselskii不动点定理给出证明，最后以实例验证结论。

Rank deficiency of Kalman error covariance matrices in linear time-varying system with deterministic evolution

We prove that for linear, discrete, time-varying, deterministic system (perfect model) with noisy outputs, the Riccati transformation in the Kalman filter asymptotically bounds the rank of the forecast and the analysis error covariance matrices to be less than or equal to the number of non-negative Lyapunov exponents of the system. Further, the support of these error covariance matrices is shown to be confined to the space spanned by the unstable-neutral backward Lyapunov vectors, providing the theoretical justification for the methodology of the algorithms that perform assimilation only in th…

Hale双线性形式的结构起源：从Green和Lagrange恒等式的视角

Structural Origin of the Hale Bilinear Form: From the Viewpoint of the Green and Lagrange Identities

通过建立与自治线性RFDE相关的Green和Lagrange恒等式，推导出Hale双线性形式，解决了原定义中的歧义并揭示了其结构起源。