통찰 - Mathematics

### Solving the Two-Dimensional Moment Problem Using the Schur Algorithm

The article presents a solution to the truncated two-dimensional moment problem using the Schur algorithm, which is based on the continued fraction expansion of the solution. The results are applicable to the two-dimensional moment problem for atomic measures.

### A Geometric Method for Finding the Roots of Quadratic Equations in the Complex Plane

This paper presents a geometric method for finding the roots of a quadratic equation in one complex variable by constructing a line and a circumference in the complex plane, using the known coefficients of the equation.

### Large Language Models Struggle to Detect Unreasonable Math Problems

Large language models (LLMs) demonstrate significant capabilities in solving math problems, but they tend to produce hallucinations when given questions containing unreasonable errors.

### Theory and Applications of the Sum-Of-Squares Technique: Optimization and Information Theory Insights

Optimization problems and information theory insights can be efficiently analyzed using the sum-of-squares technique.

### Sum-Of-Squares Technique: Theory, Applications, and Extensions to Information Theory

Sum-Of-Squares technique is a powerful tool for optimization, control, and information theory.

### Automated Importance Sampling via Optimal Control for Stochastic Reaction Networks: A Markovian Projection-based Approach

Efficiently reduce computational complexity in rare event probability estimation using Markovian Projection for Stochastic Reaction Networks.

### Differential Equation Constrained Optimization With Stochasticity

Stochastische Differentialgleichungen in Optimierung

### Sparse Cholesky Factorization for Solving Nonlinear PDEs with Gaussian Processes

Efficiently solve nonlinear PDEs using near-linear complexity algorithm with sparse Cholesky factorization.

### Sparse Cholesky Factorization for Solving Nonlinear PDEs with Gaussian Processes

Efficient algorithm for solving nonlinear PDEs using sparse Cholesky factorization with Gaussian processes.

### Homotopy Type Theory and Diagrams of ∞-Logoses

Homotopy type theory serves as an internal language for diagrams of ∞-logoses, enabling reasoning about higher-dimensional logical relations.