A Hierarchical Method for obtaining Eigenvalue Enclusures

An Interlacing Approach for Bounding the Sum of Laplacian Eigenvalues of Graphs

We apply eigenvalue interlacing techniques for obtaining lower and upper bounds for the sums of Laplacian eigenvalues of graphs, and characterize equality. This leads to generalizations of, and variations on theorems by Grone, and Grone and Merris. As a consequence we obtain inequalities involving bounds for some well-known parameters of a graph, such as edge-connectivity, and the isoperimetric number.

一种用于高精度保证下特征值边界的两阶段有限元方法

A Two-Stage Finite Element Approach for High-precision Guaranteed Lower Eigenvalue Bounds

本文提出一种两阶段有限元方法，通过高阶FEM在分级网格上生成与高阶上界同样精确的严格下特征值边界，解决了高精度保证下特征值边界的难题。

Upper bounds for the first eigenvalue of the Laplacian on non-orientable surfaces

In 1980 Yang and Yau~\cite{YY} proved the celebrated upper bound for the first eigenvalue on an orientable surface of genus $γ$. Later Li and Yau~\cite{LY} gave a simple proof of this bound by introducing the concept of conformal volume of a Riemannian manifold. In the same paper they proposed an approach for obtaining a similar estimate for non-orientable surfaces. In the present paper we formalize their argument and improve the bounds stated in~\cite{LY}.

分形边界区域上Neumann拉普拉斯算子计数函数余项的界研究

On bounds for the remainder term of counting functions of the Neumann Laplacian on domains with fractal boundary

针对分形边界区域Neumann拉普拉斯算子特征值计数函数的余项估计问题，提出基于Rayleigh商与边界附近新型叶状结构的构造性方法，并应用于Koch雪花等IFS极限集类区域。