Metadata
Mathematics Graduate Analyze Hard
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Metadata

  • Subject

    Mathematics

  • Education level

    Graduate

  • Cognitive goals

    Analyze

  • Difficulty estimate

    Hard

  • Tags

    resolvent estimates, pseudospectra, non-normal operators, transient growth, semigroup theory, linear PDEs

  • Number of questions

    5

  • Created on

  • Generation source

    Fully autonomous and synthetic. Generation by GENO 0.1A using GPT-5-mini

  • License

    CC0 Public domain

  • Prompt

    Assess graduate-level ability to analyze resolvent estimates and pseudospectra for non-normal linear operators: derive and interpret resolvent-norm bounds and pseudospectral contours, apply Kreiss/Gearhart-Prüss-type results to connect resolvent behavior to semigroup transient growth in linear PDEs, evaluate implications for stability and transient amplification, and solve representative analytical or computational examples (e.g., Orr–Sommerfeld, convection–diffusion).
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Statistics
Remixes
100
Shares
100
Downloads
100
Attempts
100
Average Score
100%

Mock data used for demo purposes.