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Expert-level digital electronics covering Boolean algebra, combinational and sequential logic, FPGA design, HDL programming, timing analysis, and digital system design.

日本語の概要は準備中です。原文の説明を表示しています。

Expert-level dynamics covering kinematics and kinetics of particles and rigid bodies, Newton-Euler equations, energy methods, impulse-momentum, and vibrations.

日本語の概要は準備中です。原文の説明を表示しています。

Expert-level applied electromagnetics covering transmission lines, waveguides, antennas, microwave circuits, EMC, and computational EM methods.

日本語の概要は準備中です。原文の説明を表示しています。

Expert-level embedded systems covering microcontrollers, RTOS, peripheral interfaces, low-power design, bare-metal programming, and embedded Linux.

日本語の概要は準備中です。原文の説明を表示しています。

Expert-level environmental engineering covering water treatment, wastewater treatment, air quality, solid waste, site remediation, and environmental regulations.

日本語の概要は準備中です。原文の説明を表示しています。

Expert-level environmental remediation covering site characterization, risk assessment, remediation technology selection, in-situ and ex-situ treatment, and regulatory closure.

日本語の概要は準備中です。原文の説明を表示しています。

Expert-level flight mechanics covering aircraft equations of motion, stability and control, performance, handling qualities, and flight simulation.

日本語の概要は準備中です。原文の説明を表示しています。

Expert-level fluid mechanics covering fluid statics, continuity, Bernoulli, Navier-Stokes, boundary layers, turbulence, pipe flow, and external aerodynamics.

日本語の概要は準備中です。原文の説明を表示しています。

Expert-level geotechnical engineering covering soil classification, shear strength, consolidation, foundation design, slope stability, and retaining structures.

日本語の概要は準備中です。原文の説明を表示しています。

Expert-level heat exchanger design covering shell and tube, plate, air coolers, heat integration, fouling, and thermal-hydraulic design methods.

日本語の概要は準備中です。原文の説明を表示しています。

Expert-level cell biology knowledge. Use when working with cell structure, organelles, cell signaling, cell cycle, cell division, cytoskeleton, membrane biology, vesicular trafficking, apoptosis, or cell biology techniques. Also use when the user mentions 'organelle', 'mitochondria', 'endoplasmic reticulum', 'Golgi', 'cytoskeleton', 'cell cycle', 'mitosis', 'meiosis', 'apoptosis', 'signal transduction', 'membrane potential', 'endocytosis', or 'cell migration'.

日本語の概要は準備中です。原文の説明を表示しています。

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'.

日本語の概要は準備中です。原文の説明を表示しています。

Expert-level quantum mechanics knowledge. Use when working with wave functions, Schrodinger equation, quantum states, operators, uncertainty principle, quantum tunneling, spin, angular momentum, perturbation theory, or quantum entanglement. Also use when the user mentions 'wave function', 'Schrodinger', 'Heisenberg', 'quantum state', 'eigenvalue', 'superposition', 'tunneling', 'spin', 'Hilbert space', 'Dirac notation', 'commutator', or 'quantum measurement'.

日本語の概要は準備中です。原文の説明を表示しています。

Expert-level probability theory knowledge. Use when working with probability spaces, random variables, distributions, expectation, variance, conditional probability, stochastic processes, Markov chains, martingales, or measure-theoretic probability. Also use when the user mentions 'sample space', 'random variable', 'expected value', 'variance', 'conditional probability', 'independence', 'Markov chain', 'Poisson process', 'moment generating function', 'law of large numbers', 'central limit theorem', or 'stochastic process'.

日本語の概要は準備中です。原文の説明を表示しています。

Expert-level plasma physics knowledge. Use when working with plasma state, Debye shielding, plasma oscillations, magnetohydrodynamics, plasma confinement, fusion plasmas, space plasmas, plasma waves, or plasma instabilities. Also use when the user mentions 'plasma', 'Debye length', 'plasma frequency', 'MHD', 'magnetic confinement', 'tokamak', 'plasma instability', 'Alfven wave', 'Langmuir probe', 'ionosphere', or 'solar wind'.

日本語の概要は準備中です。原文の説明を表示しています。

Expert-level particle physics knowledge. Use when working with the Standard Model, quarks, leptons, bosons, fundamental forces, Feynman diagrams, quantum field theory, particle accelerators, or particle detectors. Also use when the user mentions 'Standard Model', 'quark', 'lepton', 'boson', 'Higgs', 'gluon', 'neutrino', 'antimatter', 'Feynman diagram', 'QCD', 'QED', 'electroweak', 'LHC', or 'particle accelerator'.

日本語の概要は準備中です。原文の説明を表示しています。

Expert-level optimization knowledge. Use when working with linear programming, convex optimization, nonlinear programming, integer programming, dynamic programming, gradient methods, duality theory, or optimization algorithms. Also use when the user mentions 'linear programming', 'simplex method', 'convex optimization', 'Lagrangian', 'KKT conditions', 'gradient descent', 'Newton method', 'integer programming', 'dynamic programming', 'duality', 'Bellman equation', or 'branch and bound'.

日本語の概要は準備中です。原文の説明を表示しています。

Expert-level optics knowledge. Use when working with geometric optics, wave optics, interference, diffraction, polarization, lasers, fiber optics, optical instruments, or photonics. Also use when the user mentions 'reflection', 'refraction', 'Snell law', 'lens', 'mirror', 'interference', 'diffraction', 'polarization', 'laser', 'fiber optic', 'holography', 'aberration', or 'optical instrument'.

日本語の概要は準備中です。原文の説明を表示しています。

Expert-level numerical methods knowledge. Use when working with root finding, numerical integration, numerical differentiation, interpolation, numerical linear algebra, ODEs, PDEs, or optimization algorithms. Also use when the user mentions 'Newton method', 'bisection', 'Runge-Kutta', 'finite difference', 'finite element', 'interpolation', 'numerical integration', 'quadrature', 'iterative solvers', 'condition number', 'round-off error', or 'truncation error'.

日本語の概要は準備中です。原文の説明を表示しています。

Expert-level number theory knowledge. Use when working with divisibility, prime numbers, modular arithmetic, congruences, Diophantine equations, cryptography, quadratic residues, or analytic number theory. Also use when the user mentions 'prime', 'divisibility', 'modular arithmetic', 'congruence', 'GCD', 'Euler totient', 'Fermat little theorem', 'Chinese remainder theorem', 'quadratic residue', 'Diophantine equation', 'RSA', or 'prime factorization'.

日本語の概要は準備中です。原文の説明を表示しています。

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'.

日本語の概要は準備中です。原文の説明を表示しています。

Expert-level mathematical logic knowledge. Use when working with propositional logic, first-order logic, proof theory, model theory, computability theory, Godel incompleteness theorems, set theory, type theory, or formal verification. Also use when the user mentions 'formal proof', 'Godel', 'incompleteness', 'Turing machine', 'decidability', 'Zermelo-Fraenkel', 'axiom of choice', 'model theory', 'completeness theorem', 'computability', 'formal language', or 'type theory'.

日本語の概要は準備中です。原文の説明を表示しています。

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'.

日本語の概要は準備中です。原文の説明を表示しています。

Expert-level linear algebra knowledge. Use when working with vectors, matrices, determinants, eigenvalues, linear transformations, vector spaces, inner products, decompositions, or applications in machine learning and physics. Also use when the user mentions 'matrix', 'determinant', 'eigenvalue', 'eigenvector', 'linear transformation', 'vector space', 'basis', 'orthogonality', 'SVD', 'PCA', 'least squares', 'null space', or 'rank'.

日本語の概要は準備中です。原文の説明を表示しています。