「edge」の検索結果

Expert-level complex analysis knowledge. Use when working with complex functions, holomorphic functions, Cauchy's theorem, contour integration, Laurent series, residues, conformal mappings, or analytic continuation. Also use when the user mentions 'holomorphic', 'analytic', 'Cauchy theorem', 'residue', 'contour integral', 'Laurent series', 'conformal map', 'Riemann mapping', 'Mobius transformation', 'harmonic function', 'entire function', or 'meromorphic'.

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 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'.

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 topology knowledge. Use when working with topological spaces, continuity, compactness, connectedness, metric spaces, homeomorphisms, fundamental groups, homology, manifolds, or algebraic topology. Also use when the user mentions 'open set', 'closed set', 'compactness', 'connectedness', 'homeomorphism', 'homotopy', 'fundamental group', 'covering space', 'manifold', 'homology', 'Euler characteristic', or 'topological invariant'.

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 physics knowledge. Use when working with fluid statics, fluid dynamics, Bernoulli equation, viscosity, turbulence, Navier-Stokes equations, boundary layers, vorticity, compressible flow, or surface tension. Also use when the user mentions 'Bernoulli', 'Navier-Stokes', 'Reynolds number', 'turbulence', 'viscosity', 'boundary layer', 'vorticity', 'continuity equation', 'laminar flow', 'pressure', 'buoyancy', or 'surface tension'.

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 general relativity knowledge. Use when working with curved spacetime, Einstein field equations, geodesics, black holes, gravitational waves, cosmology, Schwarzschild metric, or tensor calculus. Also use when the user mentions 'Einstein field equations', 'curved spacetime', 'geodesic', 'black hole', 'event horizon', 'Schwarzschild', 'gravitational waves', 'spacetime curvature', 'Riemann tensor', 'metric tensor', 'cosmological constant', or 'gravitational lensing'.

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。

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 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 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 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 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 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 molecular biology knowledge. Use when working with DNA replication, transcription, translation, gene regulation, cloning, PCR, sequencing, CRISPR, epigenetics, or molecular techniques. Also use when the user mentions 'DNA replication', 'transcription', 'translation', 'gene expression', 'PCR', 'cloning', 'restriction enzyme', 'gel electrophoresis', 'Western blot', 'CRISPR', 'epigenetics', 'promoter', 'enhancer', or 'RNA splicing'.

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 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 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'.

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 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'.

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 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'.

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 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'.

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 analytical chemistry knowledge. Use when working with chromatography, spectroscopy, electroanalytical methods, sample preparation, quantitative analysis, calibration, statistics, or instrumental analysis. Also use when the user mentions 'HPLC', 'GC', 'mass spectrometry', 'atomic absorption', 'ICP', 'titration', 'calibration curve', 'detection limit', 'NMR', 'chromatography', 'electrochemistry', 'sample preparation', or 'method validation'.

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 biochemistry knowledge. Use when working with proteins, enzymes, metabolism, DNA, RNA, carbohydrates, lipids, cell signaling, or bioenergetics. Also use when the user mentions 'enzyme kinetics', 'metabolism', 'glycolysis', 'Krebs cycle', 'DNA replication', 'protein folding', 'amino acids', 'ATP', 'oxidative phosphorylation', 'gene expression', 'lipid bilayer', or 'signal transduction'.

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 electrochemistry knowledge. Use when working with electrochemical cells, electrode potentials, Nernst equation, electrolysis, batteries, fuel cells, corrosion, electroplating, or electroanalytical methods. Also use when the user mentions 'galvanic cell', 'electrolytic cell', 'electrode potential', 'Nernst equation', 'overpotential', 'Butler-Volmer', 'battery', 'fuel cell', 'corrosion', 'electroplating', 'cyclic voltammetry', or 'impedance spectroscopy'.

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 green chemistry knowledge. Use when working with sustainable synthesis, atom economy, solvent selection, catalysis, renewable feedstocks, waste reduction, life cycle assessment, or the 12 principles of green chemistry. Also use when the user mentions 'atom economy', 'E-factor', 'green solvent', 'catalysis', 'renewable feedstock', 'waste minimization', 'sustainable chemistry', 'life cycle assessment', 'PMI', 'solvent selection guide', or 'benign by 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。