Modeling the distribution of insulin in pancreas

Changbing Hu, Junyuan Yang, James D. Johnson, Jiaxu Li

correcthigh confidence

Category: math.DS
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper derives the eigenvalue condition det(D − e−λL M)=0 with M the fundamental solution of Y′=B(x)Y from 0 to L, rewrites it as a quadratic in Λ:=e−λL, and proves stability when both roots satisfy |Λ|>1 (Theorem 3.2). The candidate solution reproduces the same argument via an explicit fundamental-matrix factorization X(x;λ)=e−λxY(x). The determinant equation, the quadratic in Λ, and the stability criterion coincide with the paper’s derivation and conclusion .

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The derivation of the spectral condition and stability criterion is correct and aligns with standard fundamental-matrix arguments. The exposition would benefit from explicitly identifying the ordered exponential/fundamental solution when B(x) varies, and briefly discussing degenerate cases of the quadratic in Λ. These are clarity improvements rather than substantive mathematical fixes.