arXiv subjects

Guangsheng Wei

Publications and source records attributed to Guangsheng Wei.

3 recordsLinked to original sources

arXiv2025

On the inverse transmission eigenvalue problem with a piecewise $W_2^1$ refractive index

In this paper, we consider the inverse spectral problem of determining the spherically symmetric refractive index in a bounded spherical region of radius $b$. Instead of the usual case of the refractive index $ρ\in W^2_2$, by using singular Sturm-Liouville theory, we {first} discuss the case when the refractive index $ρ$ is a piecewise $ W^1_2$ function. We prove that if $\int_0^b \sqrt{ρ(r)} dr<b$, then $ρ$ is uniquely determined by all special transmission eigenvalues; if $\int_0^b \sqrt{ρ(r)} dr=b$, then all special transmission eigenvalues with some additional information can uniquely determine $ρ$. We also consider the mixed spectral problem and obtain that $ρ$ is uniquely determined from partial information of $ρ$ and the ``almost real subspectrum".

math.SP↗

arXiv2022

foREST: A Tree-based Approach for Fuzzing RESTful APIs

Representational state transfer (REST) is a widely employed architecture by web applications and cloud. Users can invoke such services according to the specification of their application interfaces, namely RESTful APIs. Existing approaches for fuzzing RESTful APIs are generally based on classic API-dependency graphs. However, such dependencies are inefficient for REST services due to the explosion of dependencies among APIs. In this paper, we propose a novel tree-based approach that can better capture the essential dependencies and largely improve the efficiency of RESTful API fuzzing. In particular, the hierarchical information of the endpoints across multiple APIs enables us to construct an API tree, and the relationships of tree nodes can indicate the priority of resource dependencies, \textit{e.g.,} it's more likely that a node depends on its parent node rather than its offspring or siblings. In the evaluation part, we first confirm that such a tree-based approach is more efficient than traditional graph-based approaches. We then apply our tool to fuzz two real-world RESTful services and compare the performance with two state-of-the-art tools, EvoMaster and RESTler. Our results show that foREST can improve the code coverage in all experiments, ranging from 11.5\% to 82.5\%. Besides, our tool finds 11 new bugs previously unknown.

cs.SE↗

arXiv2017

Inverse scattering problems where the potential is not absolutely continuous on the known interior subinterval

The inverse scattering problem for the Schr$\mathrm{\ddot{o}}$dinger operators on the line is considered when the potential is real valued and integrable and has a finite first moment. It is shown that the potential on the line is uniquely determined by the left (or right) reflection coefficient alone provided that the potential is known on a finite interval and it is not absolutely continuous on this known interval.

math.SP↗