「equilibrium」の検索結果

This skill covers game-theoretic methods in structural econometrics and industrial organization. Use when the user is working with strategic interactions, equilibrium analysis, or game-theoretic structural models — including entry games, conduct testing, auction models with strategic bidding, bargaining, or matching markets. Triggers on "Nash equilibrium", "subgame perfect", "best response", "strategic interaction", "entry game", "conduct testing", "auction", "mechanism design", "matching market", "bargaining", "BNE", "Bayesian Nash", "static game", "dynamic game", "repeated game", "multiple equilibria", "equilibrium selection", "discrete game", "oligopoly", "game-theoretic", "player", "payoff", "strategy", "dominant strategy", "Bresnahan-Reiss", "Ciliberto-Tamer", "partial identification", "set identification", or markup test.

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Chemical equilibrium, chemical kinetics, and electrochemistry — the quantitative core of physical chemistry. Covers equilibrium constants (Keq, Kc, Kp), Le Chatelier's principle, ICE tables, buffers and the Henderson-Hasselbalch equation, solubility product (Ksp) and the common-ion effect, rate laws, reaction order, integrated rate laws, half-life, the Arrhenius equation and activation energy, catalysis, redox reactions, galvanic and electrolytic cells, standard cell potentials, and the Nernst equation. Use when solving quantitative problems about how far a reaction goes (equilibrium), how fast it goes (kinetics), or how it converts chemical energy to electrical energy (electrochemistry).

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Applies game theory to multi-agent coordination protocols with advisory claims, repeated interactions, daemon-mediated correlation, and deviation penalties. Use for Nash equilibrium checks, folk-theorem cooperation analysis, correlated-equilibrium routing, and price-of-anarchy audits in strategic agent systems. NOT for consumer pricing, card-game strategy, or general microeconomics outside agent coordination.

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Expert-level statics covering equilibrium of rigid bodies, free body diagrams, trusses, frames, friction, centroids, and moments of inertia.

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Computes finite-temperature CALPHAD equilibria, phase fractions, and phase compositions from thermodynamic TDB databases using pycalphad. Use for alloy phase stability, equilibrium temperature sweeps, tie lines, lever-rule checks, or reproducible phase-fraction calculations with explicit components and mole-fraction conditions.

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Report wiki ingestion/completeness state, pending source delta, structural insights, or maintenance equilibrium. Use for remaining-work/status questions, hubs and bridges, or whether maintenance skills still have pending changes. wiki-digest summarizes learned knowledge instead.

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Use when the model setup, equilibrium concept, or proof architecture is the bottleneck for an American Economic Journal: Microeconomics (AEJ: Micro) manuscript — the central skill for a theory-first paper. Builds the model to the AEJ: Micro bar (clean, general, well-motivated result); it does not check whether your theorem is correct.

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Use when designing or auditing AAMAS experiments - self-play and population-based training, opponent selection, equilibrium and regret metrics, game-theoretic simulations, ablations, seeds, hyperparameters, compute, and claim-to-evidence fit - with emphasis on experiments that probe the interaction rather than chase a single-agent leaderboard.

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Create original relaxed black-pen graphics from concepts or visual references, including sparse illustrations, narrative scenes, animals, objects, abstract relationships, icons, and logo marks. Use when the user wants quick hand-drawn line energy, causal story staging, non-equilibrium proportion, shorthand forms, open contours, structural line drift, misregistered junctions, selective retracing, physical pen texture, or a transferable illustration system that must not collapse into clean vector minimalism or polished period-sketch drawing.

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Think and work like an expert Mechanical Engineer. Use when a task calls for Mechanical Engineer judgment. Reasons from equilibrium, failure physics, and code-backed allowables; designs through requirements, GD&T, DFMEA, and hand/FEA/test validation with explicit governing failure modes.

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Think and work like an expert Electrochemist. Use when a task calls for Electrochemist judgment. Reason from interfacial thermodynamics and transport: Nernst sets equilibrium, Butler–Volmer sets kinetics, Levich/Randles–Ševčík set mass transport, and EIS deconvolves electrode and battery interphases.

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Think and work like an expert Chemical Engineer. Use when a task calls for Chemical Engineer judgment. Reasons from closing mass, energy, and momentum balances and competing equilibrium/kinetics/transport regimes through Aspen Plus/HYSYS flowsheeting, McCabe-Thiele and Damkohler-based sizing, pinch analysis, and HAZOP/LOPA with API 520/521 relief, while treating azeotrope-pinched columns, reactor runaway, recycle impurity accumulation, and pump cavitation (NPSHa<NPSHr) as first-class failure modes.

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Think and work like an expert Biophysicist. Use when a task calls for Biophysicist judgment. Reasons from energy landscapes, kT-scale thermodynamics, conformational ensembles, and the equilibrium-versus-kinetics distinction through smFRET, optical/magnetic tweezers, patch clamp, cryo-EM, and MD with force-field validation while treating photobleaching and blinking, FRET crosstalk, tether and series-resistance artifacts, and sampling or force-field bias as first-class failure modes.

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Think and work like an expert Astrobiologist. Use when a task calls for Astrobiologist judgment. Reasons from habitability, redox disequilibrium, and Bayesian biosignature frameworks through Mars (Perseverance, Viking perchlorate lessons), Europa Clipper ocean worlds, agnostic signatures and the Ladder of Life Detection, while treating abiotic mimics, preservation, and LUCA phylogenomics as constraints—not templates—for extraterrestrial life.

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Game-theory primitives for divergent incentives: Nash equilibrium, auctions, mechanism design, collusion, bargaining, reputation. Use when modeling strategic play.

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Statics, dynamics, stress-strain analysis, materials selection, failure modes, and finite element analysis concepts for engineered structures. Covers free-body diagrams, equilibrium, internal forces (shear and moment), beam deflection, column buckling, material properties, factor of safety, fatigue, fracture mechanics, and FEA workflow. Use when analyzing loads on structures, selecting materials, predicting failure, or interpreting structural behavior.

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Foundations of individual economic decision-making, market structures, and strategic interaction. Covers supply and demand analysis, price elasticity, consumer and producer surplus, market structures (perfect competition, monopoly, oligopoly, monopolistic competition), game theory (Nash equilibrium, dominant strategies, repeated games), and welfare economics. Use when analyzing individual markets, firm behavior, pricing strategies, consumer choice, or strategic interactions between economic agents.

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Stellar structure and life cycles from birth to endpoint. Covers the Hertzsprung-Russell diagram, hydrostatic equilibrium, main-sequence physics and the mass-luminosity relation, nuclear fusion stages (pp-chain, CNO cycle, triple-alpha), nucleosynthesis, post-main-sequence evolution through red giants and the horizontal branch, and stellar endpoints — planetary nebulae, white dwarfs and the Chandrasekhar limit, supernovae, neutron stars, and black holes. Use when placing a star on the HR diagram, estimating its lifetime, predicting its fate from its mass, or teaching how a star lives and dies.

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Interact with Aptos blockchain - check balances, transfer APT, swap tokens, stake, and execute Move view functions. Features game-theoretic decision analysis with Nash equilibrium detection. All transactions require explicit approval.

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Analyze a tensegrity system by identifying compression struts and tension cables, classifying type (class 1/2, biological/architectural), computing prestress equilibrium, verifying stability via Maxwell's rigidity criterion, and mapping biological tensegrity (microtubules, actin, intermediate filaments). Use when evaluating tensegrity in architecture, robotics, cell biology, or any system with isolated compression in continuous tension.

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Build PFC 5.0 asphalt-mixture specimens with explicit aggregate objects, a declared homogenized-mastic or fine-particle abstraction, residual air voids, measured gradation conversion, contact-pair assignment, compaction, equilibrium, and mass-volume closure; use before Marshall, rutting, creep, or strength tests.

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Design and audit PFC 5.0 wall servo, loading-rate control, equilibrium checks, micro-to-macro calibration, two-target local solves, DOE campaigns, and independent confirmation for asphalt models.

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"Apply Smith and Lewis's paradox theory to identify and manage organizational tensions across performing, organizing, belonging, and learning dimensions. Use this skill when the user needs to diagnose persistent either/or tensions, design dynamic equilibrium strategies that embrace both poles, or when they ask 'why does solving this problem make it worse', 'how do we pursue exploration AND exploitation simultaneously', or 'why do our strategic tensions keep recurring despite resolution attempts'.".

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"Apply supply and demand analysis to explain price determination, market equilibrium, and the effects of policy interventions. Use this skill when the user needs to analyze how prices are set in a market, predict the effect of taxes/subsidies/price controls, or understand shifts in supply or demand curves — even if they say 'why did the price go up', 'what happens if the government sets a price cap', or 'how does a tariff affect the market'.".

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。