luo kai

Expert-level real analysis knowledge. Use when working with limits, continuity, differentiability, Riemann and Lebesgue integration, sequences and series of functions, metric spaces, measure theory, or functional analysis foundations. Also use when the user mentions 'epsilon-delta', 'uniform continuity', 'uniform convergence', 'Lebesgue integral', 'measure theory', 'sigma-algebra', 'Banach space', 'Hilbert space', 'completeness', 'compactness', 'Heine-Borel', or 'dominated convergence'.

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Expert-level discrete mathematics knowledge. Use when working with logic, set theory, combinatorics, graph theory, relations, functions, induction, recursion, boolean algebra, or discrete probability. Also use when the user mentions 'combinatorics', 'permutations', 'combinations', 'pigeonhole principle', 'inclusion-exclusion', 'generating functions', 'recurrence relations', 'graph theory', 'trees', 'logic', 'propositional calculus', or 'boolean algebra'.

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Expert-level differential equations knowledge. Use when working with ordinary differential equations, partial differential equations, systems of ODEs, Laplace transforms, Fourier methods, boundary value problems, stability analysis, or numerical methods for ODEs. Also use when the user mentions 'ODE', 'PDE', 'initial value problem', 'boundary value problem', 'Laplace transform', 'separation of variables', 'eigenvalue problem', 'heat equation', 'wave equation', 'Laplace equation', 'stability', or 'phase plane'.

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Expert-level special relativity knowledge. Use when working with Lorentz transformations, time dilation, length contraction, relativistic energy, mass-energy equivalence, spacetime, four-vectors, or relativistic mechanics. Also use when the user mentions 'Lorentz transformation', 'time dilation', 'length contraction', 'E=mc2', 'spacetime', 'four-vector', 'relativistic momentum', 'light cone', 'proper time', 'Minkowski', or 'relativistic velocity addition'.

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Expert-level condensed matter physics knowledge. Use when working with crystal structure, band theory, semiconductors, superconductivity, magnetism, phase transitions, Fermi liquids, topological materials, or strongly correlated systems. Also use when the user mentions 'band gap', 'Fermi energy', 'semiconductor', 'superconductor', 'phonon', 'crystal lattice', 'Brillouin zone', 'Bloch theorem', 'Hall effect', 'magnetism', 'phase transition', or 'topological insulator'.

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Expert-level classical mechanics knowledge. Use when working with Newton's laws, kinematics, dynamics, energy, momentum, rotational motion, oscillations, gravitation, Lagrangian mechanics, or Hamiltonian mechanics. Also use when the user mentions 'force', 'torque', 'momentum', 'energy conservation', 'simple harmonic motion', 'projectile', 'friction', 'center of mass', 'moment of inertia', 'Lagrangian', or 'Hamiltonian'.

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Expert-level calculus knowledge. Use when working with limits, derivatives, integrals, multivariable calculus, vector calculus, differential equations, series, or optimization. Also use when the user mentions 'derivative', 'integral', 'limit', 'chain rule', 'gradient', 'divergence', 'curl', 'Taylor series', 'Fourier series', 'partial derivative', 'double integral', 'line integral', 'Stokes theorem', or 'Lagrange multipliers'.

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Expert-level nuclear physics knowledge. Use when working with nuclear structure, radioactive decay, nuclear reactions, fission, fusion, binding energy, nuclear models, radiation, or nuclear applications. Also use when the user mentions 'radioactive decay', 'half life', 'binding energy', 'fission', 'fusion', 'alpha decay', 'beta decay', 'gamma decay', 'nuclear reaction', 'cross section', 'Q value', 'nuclear reactor', or 'radiation dose'.

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Expert-level computational chemistry knowledge. Use when working with molecular dynamics, density functional theory, force fields, quantum chemistry calculations, molecular docking, free energy calculations, or cheminformatics. Also use when the user mentions 'DFT', 'molecular dynamics', 'force field', 'AMBER', 'GROMACS', 'Gaussian', 'basis set', 'geometry optimization', 'molecular docking', 'free energy perturbation', 'QSAR', or 'cheminformatics'.

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Expert-level statistics knowledge. Use when working with probability distributions, hypothesis testing, regression, Bayesian statistics, statistical inference, experimental design, ANOVA, or statistical modeling. Also use when the user mentions 'p-value', 'confidence interval', 'hypothesis test', 'regression', 'ANOVA', 'chi-square', 't-test', 'Bayesian', 'maximum likelihood', 'statistical significance', 'correlation', 'normal distribution', or 'sampling distribution'.

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Expert-level thermodynamics knowledge. Use when working with heat, temperature, entropy, thermodynamic laws, heat engines, refrigerators, phase transitions, statistical mechanics, or thermodynamic cycles. Also use when the user mentions 'entropy', 'enthalpy', 'Carnot', 'heat engine', 'thermodynamic cycle', 'ideal gas', 'phase transition', 'Gibbs free energy', 'specific heat', 'thermal equilibrium', or 'second law'.

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Expert-level biochemistry from a biology perspective covering metabolic pathways, enzyme kinetics, bioenergetics, signal transduction, and the biochemical basis of cellular processes.

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