Mr Selten's work let economists whittle down the number of possible Nash equilibria.
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The fact that all such games have such equilibria, as Nash proved, is important for several reasons.
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Ice ages and runaway Arctic methane releases are examples of "multiple equilibria" — when two vastly different things can happen under the same conditions.
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Rather than noise, the mood swings reflect investors' attempts to work out which of two very different equilibria an unsettled global economy will land on.
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Equilibria has a test online where you can figure out your color, which is kind of like a Myers-Briggs classification but it's your work personality.
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While you may not have heard of the term "multiple equilibria," you've probably heard of the term for when the transition suddenly takes place: a "tipping point".
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For Coco Meers, now the founder of Equilibria — a female-focused CBD brand — angel investing was a way to stay connected with early-stage founders after she sold her first company, beauty-booking app PrettyQuick, to Groupon in 2015.
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The theory behind such stable strategy profiles, which came to be known as "Nash equilibria," revolutionized the field of game theory, altering the course of economics and changing the way everything from political treaties to network traffic is studied and analyzed.
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And so, we might hope that "games" like economic incentive packages, tax codes, treaty parameters and network designs will end in Nash equilibria, where individuals, acting in their own interest, all end up with something to be happy about, and systems are stable.
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Equilibria Mini Daily Drops; $35 for 15 ml The CBD craze can be overwhelming, but Equilibria's full-spectrum hemp flower oil CBD mixture — meant to "promote focus and decrease tension," according its website — comes with a consultation from a dosage expert to help find the right way to incorporate it into your wellness routine.
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In his famous paper, John Forbes Nash proved that there is an equilibrium for every finite game. One can divide Nash equilibria into two types. Pure strategy Nash equilibria are Nash equilibria where all players are playing pure strategies. Mixed strategy Nash equilibria are equilibria where at least one player is playing a mixed strategy.
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The set of subgame perfect equilibria for a given game is always a subset of the set of Nash equilibria for that game. In some cases the sets can be identical. The ultimatum game provides an intuitive example of a game with fewer subgame perfect equilibria than Nash equilibria.
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CPNE is related to the theory of the core. Finally in the eighties, building with great depth on such ideas Mertens-stable equilibria were introduced as a solution concept. Mertens stable equilibria satisfy both forward induction and backward induction. In a game theory context stable equilibria now usually refer to Mertens stable equilibria.
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Examples of PPAD-complete problems include finding Nash equilibria, computing fixed points in Brouwer functions, finding Arrow-Debreu equilibria in markets.
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A challenge for the use of Berge equilibria is that they do not have as strong existence properties as Nash equilibria, although their existence may be assured by adding extra conditions. The Berge equilibrium solution concept may also be used for games that do not satisfy the conditions for Nash's existence theorem and have no Nash equilibria, such as certain games with infinite strategy sets, or in situations where equilibria in pure strategies are desired and yet there are no Nash equilibria among the pure strategy profiles.
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The Cass Shell example relies on the fact that general equilibrium models often possess multiple equilibria. When this occurs, there is always an odd number of equilibria. Cass and Shell construct an example with three equilibria in period 2 and they showed that, if a subset of people cannot trade financial securities in period 1, there exist additional equilibria which are constructed as randomizations across the multiple equilibria of the original model. If, in contrast, everyone is present in period 1, these randomizations are not possible as a consequence of the first welfare theorem of economics (Fundamental theorems of welfare economics).
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Much work on sunspot equilibria aims to prove the possible existence of equilibria differing from a given model's competitive equilibria, which can result from various types of extrinsic uncertainty. The sunspot equilibrium framework supplies a basis for rational expectations modeling of excess volatility (volatility resulting from sources other than randomness in the economic fundamentals). Proper sunspot equilibria can exist in a number of economic situations, including asymmetric information, externalities in consumption or production, imperfect competition, incomplete markets, and restrictions on market participation.
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400px Similar cyclization equilibria apply to the highly reactive maleic dialdehyde.
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Fluid Phase Equilibria can be obtained in print or in electronic form.
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The field of welfare economics is associated with two fundamental theorems. The first states that given certain assumptions, competitive markets (price equilibria with transfers, e.g. Walrasian equilibria) produce Pareto efficient outcomes. The assumptions required are generally characterised as "very weak".
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The next steps in the theoretical research came with the work of John Roberts on supply-constrained equilibria at competitive prices, and then with the dissertation of Jean-Jacques Herings at Tilburg (1987, 1996). In both cases, there appear results on existence of a continuum of Drèze equilibria. Following the work of Roberts and Herings, Drèze (113) proved existence of equilibria with arbitrarily severe rationing of supply. Next, in a joint paper with Herings and others (132), Drèze established the generic existence of a continuum of Pareto-ranked supply-constrained equilibria for a standard economy with some fixed prices.
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Thus, game theory is a natural way to view the Internet and interactions within it, both human and mechanical. Game theory studies equilibria (such as the Nash equilibrium). An equilibrium is generally defined as a state in which no player has an incentive to change their strategy. Equilibria are found in several fields related to the Internet, for instance financial interactions and communication load-balancing. Game theory provides tools to analyze equilibria, and a common approach is then to ‘find the game’—that is, to formalize specific Internet interactions as a game, and to derive the associated equilibria.
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"agent- based models," The New Palgrave Dictionary of Economics, 2nd Edition. Abstract. general-equilibrium,The New Palgrave Dictionary of Economics, 2008. 2nd Edition: • "computation of general equilibria" by Herbert E. Scarf. Abstract. • "computation of general equilibria (new developments)" by Felix Kubler. Abstract.
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Of particular significance to future developments is a joint paper with Pierre Dehez (55), which establishes the existence of Drèze equilibria with no rationing of the demand side. These are called "supply-constrained equilibria". They correspond to the empirically relevant macroeconomic situations.
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Otherwise an uncorrelated asymmetry is said to exist, and the corner Nash equilibria are ESSes.
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Quasi-perfect equilibrium is a refinement of Nash Equilibrium for extensive form games due to Eric van Damme.Eric van Damme. "A relationship between perfect equilibria in extensive form games and proper equilibria in normal form games." International Journal of Game Theory 13:1--13, 1984.
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Sometimes it is an emergent pattern. Sometimes, however, it is an unintelligible mangle. In some ways, agent-based models complement traditional analytic methods. Where analytic methods enable humans to characterize the equilibria of a system, agent-based models allow the possibility of generating those equilibria.
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7 No. 3, pp. 421–443. provides a general proof that there are no asymmetric equilibria.
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Therefore, constitutions could be characterized by a self-enforcing equilibria between the rulers and powerful administrators.
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In fact, every ESS corresponds to a Nash equilibrium, but some Nash equilibria are not ESSes.
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Two or more equilibria can exist at the same time. When this is so, equilibrium constants can be ascribed to individual equilibria, but they are not always unique. For example, three equilibrium constants can be defined for a dibasic acid, H2A.The definitions given are association constants.
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Azariadis formalized and developed the idea of poverty trap. He showed that there would be multiple equilibria arising from threshold externalities in the overlapping generations model, and some of the equilibria are associated with long-lasting poverty. This novel idea envisioned the possibility of convergence clubs.
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The potential fall in efficiency from social to selfish equilibria is an example of the price of anarchy. Wardrop did not provide algorithms for solving Wardrop equilibria, he simply defined them as desiderata. The first mathematical model of network equilibrium was formulated by Beckmann, McGuire and Winsten in 1956. As with Nash equilibria, simple solutions to selfish equilibrium can be found through iterative simulation, with each agent assigning its route given the choices of the others.
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The results of that successful effort were to inspire policy recommendations in Europe for several years. The next steps in the theoretical research came with the work of John Roberts on supply-constrained equilibria at competitive prices, and then with the dissertation of Jean-Jacques Herings at Tilburg (1987, 1996). In both cases, there appear results on existence of a continuum of Drèze equilibria. Following these leads, Drèze (113) proved existence of equilibria with arbitrarily severe rationing of supply.
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But there are also other equilibria. In some the sender sends the same signal in every state and the receiver takes the action that is best to take given no additional information about the state of the world (pooling equilibria). Also, when there are more than two states, signals, and acts, there are partial pooling equilibria where some information is conveyed, but some states are also pooled.Huttegger, Simon (2007) "Evolution and Explanation of Meaning", Philosophy of Science 74(1), 1–27.
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Martimort, D., Stole, L. (2003). Contractual externalities and common agency equilibria. B.E. Journal of Theoretical Economics, 3(1).
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For 2x2 games, the set of trembling-hand perfect equilibria coincides with the set of equilibria consisting of two undominated strategies. In the example above, we see that the equilibrium is imperfect, as Left (weakly) dominates Right for Player 2 and Up (weakly) dominates Down for Player 1.
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The Nash equilibria are where both q_1 and q_2 are best responses given those values of q_1 and q_2.
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Each successive solution concept presented in the following improves on its predecessor by eliminating implausible equilibria in richer games.
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In water–heavy water mixtures equilibria several species are involved: H2O, HDO, D2O, H3O+, D3O+, H2DO+, HD2O+, HO−, DO−.
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The univariant lines of these diagrams limit the region of vapor liquid equilibria where binary distillation can be applied.
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Rescorla, Michael, "Convention", The Stanford Encyclopedia of Philosophy (Spring 2011 Edition) Conventions, he argued, are a species of coordination equilibria.
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Some have questioned the practical applicability of the general equilibrium approach based on the possibility of non-uniqueness of equilibria.
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However, some other reactions are believed to involve rapid pre-equilibria prior to the rate-determining step, as shown below.
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Rephrasing problems in terms of games allows the analysis of Internet-based interactions and the construction of mechanisms to meet specified demands. If equilibria can be shown to exist, a further question must be answered: can an equilibrium be found, and in reasonable time? This leads to the analysis of algorithms for finding equilibria.
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The pure Nash equilibria are the points in the bottom left and top right corners of the strategy space, while the mixed Nash equilibrium lies in the middle, at the intersection of the dashed lines. Unlike the pure Nash equilibria, the mixed equilibrium is not an evolutionarily stable strategy (ESS). The mixed Nash equilibrium is also Pareto dominated by the two pure Nash equilibria (since the players will fail to coordinate with non-zero probability), a quandary that led Robert Aumann to propose the refinement of a correlated equilibrium. Reaction correspondence for 2x2 coordination games.
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They have proposed many related solution concepts (also called 'refinements' of Nash equilibria) designed to overcome perceived flaws in the Nash concept. One particularly important issue is that some Nash equilibria may be based on threats that are not 'credible'. In 1965 Reinhard Selten proposed subgame perfect equilibrium as a refinement that eliminates equilibria which depend on non-credible threats. Other extensions of the Nash equilibrium concept have addressed what happens if a game is repeated, or what happens if a game is played in the absence of complete information.
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In the standard Spence signaling game, with two types of senders, a continuum of pooling equilibrium persist under solution concepts such as Sequential equilibrium and PBE. But the Cho-Kreps intuitive criterion eliminates all pooling equilibria. In the same game, there is also a continuum of separating equilibria, but the intuitive criterion eliminates all the separating equilibria except for the most efficient one - i.e. the one where low-ability types are exactly indifferent between acquiring the amount of education that high-ability types do, and not acquiring any education at all.
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"Punctuated equilibria: an alternative to phyletic gradualism" In T.J.M. Schopf, ed., Models in Paleobiology. San Francisco: Freeman Cooper. pp. 82-115.
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If condition one does not hold then the equilibrium is unstable. If only condition one holds then there are likely to be an infinite number of optimal strategies for the player who changed. In the "driving game" example above there are both stable and unstable equilibria. The equilibria involving mixed strategies with 100% probabilities are stable.
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Sequential equilibrium is a further refinement of subgame perfect equilibrium and even perfect Bayesian equilibrium. It is itself refined by extensive-form trembling hand perfect equilibrium and proper equilibrium. Strategies of sequential equilibria (or even extensive-form trembling hand perfect equilibria) are not necessarily admissible. A refinement of sequential equilibrium that guarantees admissibility is quasi- perfect equilibrium.
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As of 2015, there is not a coherent analytical theory for three-dimensional equilibria. The general approach to finding three-dimensional equilibria is to solve the vacuum ideal MHD equations. Numerical solutions have yielded designs for stellarators. Some machines take advantage of simplification techniques such as helical symmetry (for example University of Wisconsin's Helically Symmetric eXperiment).
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While Nash proved that every finite game has a Nash equilibrium, not all have pure strategy Nash equilibria. For an example of a game that does not have a Nash equilibrium in pure strategies, see Matching pennies. However, many games do have pure strategy Nash equilibria (e.g. the Coordination game, the Prisoner's dilemma, the Stag hunt).
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Fluid Phase Equilibria is a peer-reviewed scientific journal on physical chemistry and thermodynamics that is published by Elsevier. The articles deal with experimental, theoretical and applied research related to properties of pure components and mixtures, especially phase equilibria, caloric and transport properties of fluid and solid phases. It has an impact factor of 2.838 (2019).
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Therefore, when dealing with such dynamical systems one can use the simpler linearisation of the system to analyse its behaviour around equilibria.
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"Punctuated equilibria: an alternative to phyletic gradualism." In T.J.M. Schopf, ed., Models in Paleobiology. San Francisco: Freeman, Cooper and Company, pp. 82-115.
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Acid–base equilibria are important in a very wide range of applications, such as acid–base homeostasis, ocean acidification, pharmacology and analytical chemistry.
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His research has focused on small particle science and technology, the development of particle-based advanced materials, and polymeric advanced materias. His work has focused on applied problems in dispersion and materials technology for advanced coatings in imaging, antifouling, corrosion mitigation, and antimicrobial prophylaxis. He has made significant contributions to the understanding of microemulsion structure and the complex equilibria that exist among the exotic molecular complexes contained in microemulsions, as well as in microemulsion polymerization. Seminal self-diffusion studies done with collaborators at Eastman Kodak produced order parameters that proved transitions among such complex equilibria are continuous phase transitions (chemical equilibria).
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On the other hand, a person in the situation of B might give A his money, fearing that A is not rational, or might even be suicidal. A non-credible threat is made on the hope that it will be believed, and therefore the threatening undesirable action will not need to be carried out. For a threat to be credible within an equilibrium, whenever a node is reached where a threat should be fulfilled, it will be fulfilled. Those Nash equilibria that rely on non-credible threats can be eliminated through backward induction; the remaining equilibria are called subgame perfect Nash equilibria.
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In turn this changes > the set of equilibria. Put more succinctly, the set of equilibria is path > dependent... [This path dependence] makes the calculation of equilibria > corresponding to the initial state of the system essentially irrelevant. > What matters is the equilibrium that the economy will reach from given > initial endowments, not the equilibrium that it would have been in, given > initial endowments, had prices happened to be just right (Franklin > Fisher).As quoted by The Arrow–Debreu model in which all trade occurs in futures contracts at time zero requires a very large number of markets to exist.
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Next, in a joint paper with Herings and others (132), the generic existence of a continuum of Pareto- ranked supply-constrained equilibria was established for a standard economy with some fixed prices. An intuitive explanation of that surprising result is this: if some prices are fixed and the remaining are flexible, the level of the latter prices relative to the former introduces a degree of freedom that accounts for the multiplicity of equilibria; globally, less rationing is associated with a higher price level; the multiplicity of equilibria thus formalises a trade-off between inflation and unemployment, comparable to a Phillips curve.
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This result was called the Folk Theorem because it was widely known among game theorists in the 1950s, even though no one had published it. Friedman's (1971) Theorem concerns the payoffs of certain subgame-perfect Nash equilibria (SPE) of an infinitely repeated game, and so strengthens the original Folk Theorem by using a stronger equilibrium concept: subgame-perfect Nash equilibria rather than Nash equilibria. The Folk Theorem suggests that if the players are patient enough and far-sighted (i.e. if the discount factor \delta \to 1 ), then repeated interaction can result in virtually any average payoff in an SPE equilibrium.
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These results are taken to show that subgame perfect equilibria and Nash equilibria fail to predict human play in some circumstances. The Centipede game is commonly used in introductory game theory courses and texts to highlight the concept of backward induction and the iterated elimination of dominated strategies, which show a standard way of providing a solution to the game.
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However, if this short-run equilibrium price is sufficiently high, production will be very profitable, and capacity will increase. This shifts the short-run supply schedule to the right, and a new short-run equilibrium price will be obtained. The resulting sequence of short-run equilibria are termed temporary equilibria. The overall system involves two state variables: price and capacity.
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Finally, in two studies with Lars Stole, Martimort shows that all common agency equilibria can be characterized by an extension of the taxation principle - the "delegation principle" -Martimort, D., Stole, L. (2002). The revelation and delegation principles in common agency games. Econometrica, 70(4), pp. 1659-1673. and how those equilibria are affected by direct externalities between principals under nonlinear price competition.
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It is noteworthy, that the price indeterminacy that evolves from multiple price equilibria is fundamentally different from price indeterminacy that stems from market incompleteness.
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In symmetric games, when the players have a strategy and action sets which are mirror images of one another, often the analysis focuses on symmetric equilibria, where all players play the same mixed strategy. As in the rest of game theory, this is done both because these are easier to find analytically and because they are perceived to be stronger focal points than asymmetric equilibria.
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Then, in equilibrium, the agents may exchange some apples for an equal number of guavas, and the result will still be an equilibrium. For example, if there is an equilibrium in which Alice holds 4 apples and 2 guavas and George holds 5 apples and 3 guavas, then the situation in which Alice holds 5 apples and 1 guava and George 4 apples and 4 guavas is also an equilibrium. But, in both these equilibria, the total utilities of both agents are the same: Alice has utility 6 in both equilibria, and George has utility 8 in both equilibria. This is not a coincidence, as shown in the following section.
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Sunspot equilibria are closely connected to the possibility of indeterminacy in dynamic economic models. In a general equilibrium model with a finite number of commodities, there is always a finite odd number of equilibria, each of which is isolated from every other equilibrium. In models with an infinite number of commodities, and this includes most dynamic models, an equilibrium can be characterized by a bounded sequence of price vectors. When the set of traders changes over time, as it must in any model with birth and death, there are typically open sets of indeterminate equilibria where, arbitrarily close to one equilibrium, there is another one.
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Gunnthorsdottir Anna, Vragov Roumen, Seifert Stefan and Kevin McCabe 2010 "Near-efficient equilibria in contribution-based competitive grouping," Journal of Public Economics, 94, pp. 987-994.
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Games like the driving example above have illustrated the need for solution to coordination problems. Often we are confronted with circumstances where we must solve coordination problems without the ability to communicate with our partner. Many authors have suggested that particular equilibria are focal for one reason or another. For instance, some equilibria may give higher payoffs, be naturally more salient, may be more fair, or may be safer.
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Another simple example is the finitely repeated prisoner's dilemma for T periods, where the payoff is averaged over the T periods. The only Nash equilibrium of this game is to choose Defect in each period. Now consider the two strategies tit-for-tat and grim trigger. Although neither tit-for-tat nor grim trigger are Nash equilibria for the game, both of them are \epsilon-equilibria for some positive \epsilon.
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In an economy with externalities, for example, it is possible for equilibria to arise that are not efficient. The first welfare theorem is informative in the sense that it points to the sources of inefficiency in markets. Under the assumptions above, any market equilibrium is tautologically efficient. Therefore, when equilibria arise that are not efficient, the market system itself is not to blame, but rather some sort of market failure.
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Given that equilibria may not be unique, it is of some interest to ask whether any particular equilibrium is at least locally unique. If so, then comparative statics can be applied as long as the shocks to the system are not too large. As stated above, in a regular economy equilibria will be finite, hence locally unique. One reassuring result, due to Debreu, is that "most" economies are regular.
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Of particular significance to future developments is a joint paper with Pierre Dehez (55), which establishes the existence of Drèze equilibria with no rationing of the demand side. These are called "supply- constrained equilibria". They correspond to the empirically relevant macroeconomic situations. In the meantime, Jean-Pascal Bénassy (1975) and Yves Younès (1975) had approached the same problem from a macroeconomic angle, for the more restrictive case of fixed prices.
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During the early part of his career he was influenced by the ideas of Lars Gunnar Sillén and Robert Garrels regarding aqueous chemical equilibria. He developed models where the ideas by Sillén regarding equilibria were combined with improved descriptions of kinetically controlled reactions (i.e. slow reactions that do not reach equilibrium, e.g. weathering). He in particular made contributions to the knowledge of the reactions at the interface of minerals and water.
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The facility-location game may have other pure Nash equilibria, in which the social welfare is not maximal. However, it is possible to prove that the social welfare in such equilibria is at least half the optimum. Therefore, the price of anarchy is at most 2. Moreover, it is possible to show that the price-of-anarchy is at most 2 even when the game does not converge to equilibrium.
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Non-linear I and S functions generated by different behavior at different parts of the cycle. Non-linear I and S functions lead to multiple, shifting equilibria. Shifting, multiple equilibria lead to six-stage business cycle in which the economy oscillates around optimal income growth and generates phases of boom and bust. After the publication of John Maynard Keynes' General Theory many attempts were made to build a business cycle model.
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If a stage-game in a finitely repeated game has multiple Nash equilibria, subgame perfect equilibria can be constructed to play non-stage-game Nash equilibrium actions, through a "carrot and stick" structure. One player can use the one stage-game Nash equilibrium to incentivize playing the non-Nash equilibrium action, while using a stage-game Nash equilibrium with lower payoff to the other player if they choose to defect.
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The Ga-Sb phase equilibria was investigated in 1955 by KosterKoster, W.; Thoma, B., Z. Metallkd. 46, 291 (1955). and by Greenfield.Greenfield, I. G.; Smith, R. L., Trans.
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The paper demonstrated that in static Arrow-Debreu economies with complete markets, extrinsic uncertainty (where no fundamentals of the model are stochastic) cannot matter to equilibrium allocations. They then showed that when some agents were restricted in their trades, so that market completeness was violated, sunspots could matter, i.e. there could exist rational expectations equilibria in which equilibrium prices depended on the realization of an extrinsic stochastic process. In passing, they made the observation that since the validity of the first welfare theorem implied that there could be no sunspot equilibria, a necessary condition for the existence of such equilibria was a violation of the conditions under which the first welfare theorem holds.
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In classical non- cooperative game theory a coordination game is any game with multiple Nash equilibria. The literature regarding pseudo-telepathy occasionally refers to games such as the Mermin–Peres game as coordination games. On one hand, this is technically correct, because the classic variant of the Mermin–Peres game does feature multiple Nash equilibria. However, quantum pseudo-telepathy does not provide any solution to the coordination problems which characterize coordination games.
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Other areas are also touched. In game theory, John Nash used the theorem to prove that in the game of Hex there is a winning strategy for white.For context and references see the article Hex (board game). In economics, P. Bich explains that certain generalizations of the theorem show that its use is helpful for certain classical problems in game theory and generally for equilibria (Hotelling's law), financial equilibria and incomplete markets.
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Equilibrium problems model questions arising in the study of economic equilibria in a mathematically abstract form. Equilibrium problems include Variational Inequalities, problems with Nash Equilibria, and Multiple Optimization Problems with Equilibrium Constraints (MOPECs). Use EMP's keywords to reformulate these problems as mixed complementarity problems (MCPs), a class of problems for which mature solver technology exists. Solve the newly reformulated EMP keyword version of the problem with the PATH solver or other GAMS MCP solvers.
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The concept of effective demand or supply becomes relevant when markets do not continuously maintain equilibrium prices.Hal Varian, 1977. "Non-Walrasian equilibria," Econometrica, April, 573-590.Robert W. Clower, 1965.
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Martin B. Smith, Journal of Organometallic Chemistry, The Monomer-Dimer Equilibria of Liquid Ammonium Alkyls II Triisobutylaluminum Journal of Organometallic Chemistry, Volume 22, Issue 2, April 1970, Pages 273-281.
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The inorganic carbon compounds exist in equilibrium that depends on the pH of the water.Stumm, W., and Morgan, J. J. (1996). Aquatic Chemistry: Chemical Equilibria and Rates in Natural Waters.
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The collaborative work with Richard C. Tolman led to the discovery of Stewart–Tolman effect. Later he worked on acid-base equilibria of organic nitrogen compounds, as well as reaction kinetics.
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In game theory, coordination games are a class of games with multiple pure strategy Nash equilibria in which players choose the same or corresponding strategies. If this game is a coordination game, then the following inequalities hold in the payoff matrix for player 1 (rows): A > B, D > C, and for player 2 (columns): a > c, d > b. See Fig. 1. In this game the strategy profiles {Left, Up} and {Right, Down} are pure Nash equilibria, marked in gray.
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Markov perfect equilibria are not stable with respect to small changes in the game itself. A small change in payoffs can cause a large change in the set of Markov perfect equilibria. This is because a state with a tiny effect on payoffs can be used to carry signals, but if its payoff difference from any other state drops to zero, it must be merged with it, eliminating the possibility of using it to carry signals.
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Trioctylamine is used to extract organic acids such as succinic acid and acetic acid, and also precious metals. A formulation containing metoxuron mixed with an emulsion containing trioctylamine 50%, atlox 4851 B 15%, and isopropanol 35% was active as a potato defoliant. Trioctylamine can be used to extract monocarboxylic acid for equilibria and correlation of apparent reactive equilibrium constant. Liquid-liquid equilibria for aqueous solutions of carboxylic acids with trioctylamine in various diluents was determined at various trioctylamine concentrations.
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Because living systems are open systems, with continually altering fluxes of matter–energy and information, many of their equilibria are dynamic—situations identified as steady states or flux equilibria. Miller identifies the comparable matter–energy and information processing critical subsystems. Elaborating on the eight hierarchical levels, he defines society, which constitutes the seventh hierarchy, as "a large, living, concrete system with [community] and lower am levels of living systems as subsystems and components".Miller 1978, p. 747.
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Fig. 10. An Edgeworth box with multiple equilibria Fig. 11. An Edgeworth box with multiple equilibria (detail) It might be supposed from economic considerations that if a shared tangent exists through a given endowment, and if the indifference curves are not pathological in their shape, then the point of tangency will be unique. This turns out not to be true. Conditions for uniqueness of equilibrium have been the subject of extensive research: see General equilibrium theory. Figs.
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M. Goemans, V. Mirrokni, A. Vetta, Sink equilibria and convergence, FOCS 05 The term Price of Anarchy was first used by Elias Koutsoupias and Christos Papadimitriou, but the idea of measuring inefficiency of equilibrium is older.P. Dubey. Inefficiency of Nash equilibria. Math. Operat. Res., 11(1):1–8, 1986 The concept in its current form was designed to be the analogue of the 'approximation ratio' in an approximation algorithm or the 'competitive ratio' in an online algorithm.
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Phase Equilibria Diagrams Database In 1991 the Japanese database Interglad was created, followed by the publication of the "Handbook of Glass Data" in 1993."Handbook of Glass Data", edited by O. V. Mazurin, M. V. Streltsina, and T. P. Shvaiko-Shvaikovskaya, Elsevier, 1993 The "Handbook of Glass Data" was later digitalized and substantially expanded under the name SciGlass.SciGlass Currently, SciGlass contains properties of about 350,000 glass compositions, INTERGLAD about 300,000, and "Phase Equilibria Diagrams" includes about 20,000 diagrams.
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"Monetary equilibria", ch. 5 in Debreu, G., Neuefeind, W. and Trockel, W. (eds.), Economics Essays. A Festschrift for Werner Hildenbrand, Berlin: Springer. etc. ) have an effect when introduced when markets are incomplete.
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Gustav Heinrich Johann Apollon Tammann ( – 17 December 1938) was a prominent Baltic German chemist-physicist who made important contributions in the fields of glassy and solid solutions, heterogeneous equilibria, crystallization, and metallurgy.
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In the case of ternary isothermal liquid-liquid equilibria, the spinodal curve (obtained from the Hessian matrix) and the corresponding critical point can be used to help the experimental data correlation process.
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CIP Press (English translation). His hypothesis of frozen plasticity is an extension of Niles Eldredge and Stephen Jay Gould's theory of punctuated equilibria,Flegr, Jaroslav (1999). Frozen Evolution, pp. 141-146, 149-156.
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Then how can a cancer cell evolve in such a short time? Perhaps, as has been suggested,Eldredge N, Gould SJ. Punctuated equilibria: an alternative to phyletic gradualism. Models Paleobiol. 82 115 (1972).
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In Natural Selection: Domains, Levels and Challenges. p. 128. New York: Oxford University Press. and others,Eldredge, Niles; Gould, Stephen J. (1972). "Punctuated equilibria: an alternative to phyletic gradualism" In Schopf, T.J.M., ed.
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Process Engineering involves utilization of multiple tools and methods. Depending on the exact nature of the system, processes need to be simulated and modeled using mathematics and computer science. Processes where phase change and phase equilibria are relevant require analysis using the principles and laws of thermodynamics to quantify changes in energy and efficiency. In contrast, processes that focus on the flow of material and energy as they approach equilibria are best analyzed using the disciplines of fluid mechanics and transport phenomena.
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An intuitive explanation of that surprising result is this: if some prices are fixed and the remaining are flexible, the level of the latter prices relative to the former introduces a degree of freedom that accounts for the multiplicity of equilibria; globally, less rationing is associated with a higher price level; the multiplicity of equilibria thus formalises a trade-off between inflation and unemployment, comparable to a Phillips curve. In this analysis, the continuum is interpreted as reflecting co-ordination failures, not short-run price dynamics à la Phillips. The fact that price-wage rigidities can sustain co-ordination failures adds a new twist to explanations of involuntary unemployment. At the same time, multiple equilibria create problems for the definition of expectations, and introduce a new dimension of uncertainty.
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Starr first published the Shapley–Folkman lemma on the existence of quasi-equilibria in economies with non-convexities. In addition to publications in economic journals, he wrote the textbook General Equilibrium Theory: An Introduction.
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Eldredge, Niles; Gould, Stephen J. (1977) "Punctuated equilibria: the tempo and mode of evolution reconsidered." Paleobiology 3 115–151.McCarthy, T. & Rubridge, B. (2005) The Story of Earth and Life. Cape Town: Struik Publishers. .
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Mark S. Ghiorso (born October 21, 1954) is an American geochemist who resides in Seattle, Washington. He is best known for creating MELTS, a software tool for thermodynamic modeling of phase equilibria in magmatic systems.
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Mixed strategies are still widely used for their capacity to provide Nash equilibria in games where no equilibrium in pure strategies exists, but the model does not specify why and how players randomize their decisions.
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Additionally, the only intermediate observed by NMR spectroscopy is the covalent triflate 3, indicating that the complete set of equilibria between 3, the CIP 4, and SSIP 5 set is very heavily biased towards 3.
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This game has two pure strategy Nash equilibria, one where both go to the opera and another where both go to the football game. There is also a mixed strategies Nash equilibrium in both games, where the players go to their preferred event more often than the other. For the payoffs listed in the first game, each player attends their preferred event with probability 3/5. This presents an interesting case for game theory since each of the Nash equilibria is deficient in some way.
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Then define a strategy set S (in a base game) as being trembling hand perfect if there is a sequence of perturbed games that converge to the base game in which there is a series of Nash equilibria that converge to S. Note: All completely mixed Nash equilibria are perfect. Note 2: The mixed strategy extension of any finite normal-form game has at least one perfect equilibrium.Selten, R.: Reexamination of the perfectness concept for equilibrium points in extensive games. Int. J. Game Theory4, 1975, 25–55.
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Games and Economic Behavior. 14, pages 308-314, 2019. and independence of clones. Maximal lotteries are equivalent to mixed maximin strategies (or Nash equilibria) of the symmetric zero-sum game given by the pairwise majority margins.
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"Atlas of electrochemical equilibria in aqueous solutions". 2nd English edition. [Houston, TX: National Association of Corrosion Engineers.] so at any one time there may be one or more different chemical reactions occurring within a concrete structure.
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Ugo Pagano and Robert Rowthorn Pagano U (1992) Organizational equilibria and production efficiency. Metroeconomica 43: 227–246.Pagano U, Rowthorn R (1994) Ownership, technology and institutional stability. Structural Change and Economic Dynamics 5(2): 221–242.
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Phyletic gradualism is a model of evolution which theorizes that most speciation is slow, uniform and gradual.Eldredge, N. and S. J. Gould (1972). "Punctuated equilibria: an alternative to phyletic gradualism" In T.J.M. Schopf, ed., Models in Paleobiology.
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Mertens, Jean-François, 1992. "The Small Worlds Axiom for Stable Equilibria," Games and Economic Behavior, 4: 553-564. emphasized also the importance of the small worlds principle that a solution concept should depend only on the ordinal properties of players' preferences, and should not depend on whether the game includes extraneous players whose actions have no effect on the original players' feasible strategies and payoffs. Kohlberg and Mertens demonstrated via examples that not all of these properties can be obtained from a solution concept that selects single Nash equilibria.
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In the centipede game, a pure strategy consists of a set of actions (one for each choice point in the game, even though some of these choice points may never be reached) and a mixed strategy is a probability distribution over the possible pure strategies. There are several pure strategy Nash equilibria of the centipede game and infinitely many mixed strategy Nash equilibria. However, there is only one subgame perfect equilibrium (a popular refinement to the Nash equilibrium concept). In the unique subgame perfect equilibrium, each player chooses to defect at every opportunity.
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The Bertrand model can be extended to include product or location differentiation but then the main result – that price is driven down to marginal cost – no longer holds. With search costs, there may be other equilibria apart from the competitive price – the monopoly price or even price dispersion may be equilibria as in the classic "Bargains and Rip- offs" model. The model also ignores capacity constraints. If a single firm does not have the capacity to supply the whole market then the "price equals marginal cost" result may not hold.
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In the area of game theory, more specifically of non-cooperative games, Lipton together with E. Markakis and A. Mehta provedRichard Lipton, Evangelos Markakis, Aranyak Mehta (2007) "Playing Games with Simple Strategies", "EC '03: Proceedings of the 4th ACM conference on Electronic commerce", "ACM" the existence of epsilon- equilibrium strategies with support logarithmic in the number of pure strategies. Furthermore, the payoff of such strategies can epsilon-approximate the payoffs of exact Nash equilibria. The limited (logarithmic) size of the support provides a natural quasi-polynomial algorithm to compute epsilon- equilibria.
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Hellwig studied the effects of exogenous and endogenous public information in global coordination games and showed that multiplicity of equilibria is restored under fairly general conditions. Global coordination games belong to a subfield of game theory which started with the article by Morris and Shin (1998). Steven Morris and Hyun Song Shin considered a stylized currency crises model, in which traders observe the relevant fundamentals with small noise, and show that this leads to the selection of a unique equilibrium. This result is in stark contrast with models of complete information, which feature multiple equilibria.
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Figure 1. Reaction correspondence for player Y in the Stag Hunt game. Reaction correspondences, also known as best response correspondences, are used in the proof of the existence of mixed strategy Nash equilibria (, Section 1.3.B; , Section 2.2).
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Earth and Planetary Science Letters 242, 111–129.Prakash,D., Arima, M.and Mohan, A.2006, UHT metamorphism in the Palni Hills, South India: Insights from feldspar thermometry and phase equilibria. International Geology Review, v. 48, pp. 619-638.
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The study directly challenges phyletic gradualism and punctuated equilibrium. It shows how many factors can come into play when comparing the two modes of evolution.Johnson, J. G. (1982). Occurrence of phyletic gradualism and punctuated equilibria through geologic time.
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14, pp. 1253–1267, 1986 · A. Braverman, “Consumer Search and Alternative Market Equilibria”, Review of Economic Studies, Vol. 47, pp. 487–502, 1980 · A. Braverman and T.N. Srinivasan, “Credit and Sharecropping in Agrarian Societies”, Journal of Development Economics, Vol.
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The price of anarchy can be \Omega(n). Consider the following network design game. Pathological Price of Stability game Consider two different equilibria in this game. If everyone shares the 1 + \varepsilon edge, the social cost is 1 + \varepsilon.
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Arrow motivated his paper by reference to the need to extend proofs to cover equilibria at the edge of the space, and Debreu by the possibility of indifference curves being non-differentiable. Modern texts follow their style of proof.
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Recrystallization from the rain is probably responsible. Fluorosilicate minerals are thermodynamically unstable in soil.Elrashidi, M.A. and Lindsay, W.L. (1986) Chemical Equilibria of Fluorine in Soils: A Theoretical Development. Soil Science: An Interdisciplinary Approach to Soil Research, 141, 274–280.
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The theorem aims to justify a puzzling aspect of mixed strategy Nash equilibria: that each player is wholly indifferent amongst each of the actions he puts non-zero weight on, yet he mixes them so as to make every other player also indifferent. The mixed strategy equilibria are explained as being the limit of pure strategy equilibria for a disturbed game of incomplete information in which the payoffs of each player are known to themselves but not their opponents. The idea is that the predicted mixed strategy of the original game emerge as ever improving approximations of a game that is not observed by the theorist who designed the original, idealized game. The apparently mixed nature of the strategy is actually just the result of each player playing a pure strategy with threshold values that depend on the ex-ante distribution over the continuum of payoffs that a player can have.
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A significant part of Tian's research has been focused on characterization of the existence of equilibrium in discontinuous games. Tian and his co-authors systematically studied the existence of Nash equilibrium in discontinuous games, and characterized the existence of Nash equilibrium by weakening the traditional continuity, convexity and transitivity assumptions. By using very weak properties of continuity, convexity and transitivity: transfer continuity, transfer convexity, and transfer transitivity, he, along with Michael R. Baye and Jianxin Zhou, was the first to characterize the existence of Nash equilibria for discontinuous and non-convex games. In a paper published in 2015 entitled 'On The Existence of Equilibria in Games with Arbitrary Strategy Spaces and Preferences', Tian provided a full characterization on the existence of Nash equilibria in games with arbitrary strategy spaces and preferences that may be non-total, non-transitive, discontinuous, non-convex, or non-monotonic.
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This setup can be extended for more than two strategies (strategies are usually sorted so that the Nash equilibria are in the diagonal from top left to bottom right), as well as for a game with more than two players.
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He received a Guggenheim Fellowship in 2017 and the Kalai Prize in 2016. Roughgarden is a co-editor of the 2016 textbook Algorithmic Game Theory, as well as author of two chapters on the inefficiency of equilibria and routing games.
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Equipped with the activity coefficients and a knowledge of the constituents and their relative amounts, phenomena such as phase separation and vapour-liquid equilibria can be calculated. UNIFAC attempts to be a general model for the successful prediction of activity coefficients.
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Basic questions in general equilibrium analysis are concerned with the conditions under which an equilibrium will be efficient, which efficient equilibria can be achieved, when an equilibrium is guaranteed to exist and when the equilibrium will be unique and stable.
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In simultaneous move game settings, all the players declare at the same time to whom they want to link. Even though these sorts of games are easy to understand and analyze, their drawback is that they have multiple Nash Equilibria.
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The theory of response reactions (RERs) or response equilibria was elaborated for the thermodynamic systems in which more than one equilibrium is established simultaneously.1\. Fishtik, I.; Nagypál, I.; Gutman, I. J. Chem. Soc. Faraday Trans. 1995, 91, 259-267.
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The Redlich–Kwong equation has undergone many revisions and modifications, in order to either improve its accuracy in terms of predicting gas-phase properties of more compounds, as well as in better simulating conditions at lower temperatures, including vapor–liquid equilibria.
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One study focuses on how efforts to apply only one mode of evolution to a phenomenon can be inaccurate.von Vaupel Klein, J. C. (1994). Punctuated equilibria and phyletic gradualism: Even partners can be good friends. Acta Biotheoretica, 42(1), 15-48.
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Stephen Morris and Hyun Song Shin (1998)Stephen Morris and Hyun Song Shin (1998), "Unique Equilibrium in a Model of Self-Fulfilling Currency Attacks," American Economic Review, 88 (3): 587–97. considered a stylized currency crises model, in which traders observe the relevant fundamentals with small noise, and show that this leads to the selection of a unique equilibrium. This result overturns the result in models of complete information, which feature multiple equilibria. One concern with the robustness of this result is that the introduction of a theory of prices in global coordination games may reintroduce multiplicity of equilibria (Atkeson, 2001).
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Consider the version of "Chicken" pictured in Figure 6. Like all forms of the game, there are three Nash equilibria. The two pure strategy Nash equilibria are (D, C) and (C, D). There is also a mixed strategy equilibrium where each player Dares with probability 1/3. It results in expected payoffs of 14/3 = 4.667 for each player. Now consider a third party (or some natural event) that draws one of three cards labeled: (C, C), (D, C), and (C, D). This exogenous draw event is assumed to be uniformly at random over the 3 outcomes.
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In cooperative game theory, the Kalai-Smorodinsky solution reopened the study of bargaining by showing that the long unchallenged Nash solution is not unique. He later axiomatized the Egalitarian solution to bargaining problems and, with Dov Samet, formulated its extension to general (NTU) cooperative games, unifying it with the Shapley (TU) Value. In non cooperative game theory, the Kalai and Lehrer model of rational learning showed that rational players with truth-compatible beliefs eventually learn to play Nash equilibria of repeated games. In particular, in Bayesian equilibria of repeated games all relevant private information eventually becomes common knowledge.
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In contrast to the tension zone model, the bounded hybrid superiority hypothesis predicts that hybrid fitness is enhanced in environments that are intermediate between those of the parental populations or lineages, yielding 'hybrid superiority'. Another model for a persistent hybrid zone is the ecotonal model, in which a hybrid zone occurs over an environmental gradient with each parental lineage being adapted to one part of that gradient. The frequency of alleles finding different equilibria therefore depends on the precise environmental conditions in a particular area. In each location, selection maintains a stable equilibria for each allele, resulting in a smooth cline.
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Nash pictured in 2011 In 1978, Nash was awarded the John von Neumann Theory Prize for his discovery of non-cooperative equilibria, now called Nash Equilibria. He won the Leroy P. Steele Prize in 1999. In 1994, he received the Nobel Memorial Prize in Economic Sciences (along with John Harsanyi and Reinhard Selten) as a result of his game theory work as a Princeton graduate student.Nasar (2002), p. xiii. In the late 1980s, Nash had begun to use email to gradually link with working mathematicians who realized that he was John Nash and that his new work had value.
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Then the equilibrium of the system comprising and – and thus the institutional arrangement across them – is uniquely determined by preference (technology). However, there can also be cases in which neither rule dominates the other in either domain in the sense described above. If so, the agents in both domains need to take into account which rule is institutionalized in the other domain. Under the supermodularity condition there can then be two pure Nash equilibria (institutional arrangements) for the system comprising and , namely and . When such multiple equilibria exist, we say that and , as well as and , are “institutional complements”.
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This saddle point rests at the top of a barrier between two different low-energy equilibria of a given system; the two equilibria are labeled with two different baryon numbers. One of the equilibria might consist of three baryons; the other, alternative, equilibrium for the same system might consist of three antileptons. In order to cross this barrier and change the baryon number, a system must either tunnel through the barrier (in which case the process is a type of instanton process) or must for a reasonable period of time be brought up to a high enough energy that it can classically cross over the barrier (in which case the process is termed a "sphaleron" process and can be modeled with an eponymous sphaleron particle). In both the instanton and sphaleron cases, the process can only convert groups of three baryons into three antileptons (or three antibaryons into three leptons) and vice versa.
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Sample network graph. Values on edges are the travel time experienced by a 'car' traveling down that edge. is the number of cars traveling via that edge. An application of Nash equilibria is in determining the expected flow of traffic in a network.
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A real Wicksell effect also refers to a change in relative prices corresponding to a change in income distribution, but it in addition takes into account the problem of choice of technique. The "changes" under consideration are comparisons of long period equilibria.
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Rearrangement to tricyclic isomer 7 occurred, and further warming to room temperature yielded perfluorotropilidene (8). The parent quadricyclane (9) rearranges instead to norbornadiene (10), under far more vigorous conditions. unique chemistry of perfluoroquadricyclane Keto-enol equilibria are affected dramatically by fluorine substitution.
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Evolutionary systems are characterized by "moving equilibria and the dynamics of coevolutionary interactions which can not be foreseen ex ante."Rammel, Christian, and Jeroen CJM van den Bergh. "Evolutionary policies for sustainable development: adaptive flexibility and risk minimising." Ecological Economics 47.2 (2003): 121-133.
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He studied Chemistry and Physical Metallurgy at the University of Stuttgart and the Max Planck Institute for Metals Research. He received his master's degree (Dipl.-Ing) in 1956 and finished his dissertation (Dr. rer. nat.) on Phase Equilibria of Quarternary Metallic Systems in 1959.
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X-ray scattering can also yield information on the average spacing between individual lipid molecules, which has led to its use in characterizing phase transitions.D. M. Small."Phase equilibria and structure of dry and hydrated egg lecithin " Journal of Lipid Research. 8. (1967) 551-557.
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The concept of stability, useful in the analysis of many kinds of equilibria, can also be applied to Nash equilibria. A Nash equilibrium for a mixed-strategy game is stable if a small change (specifically, an infinitesimal change) in probabilities for one player leads to a situation where two conditions hold: # the player who did not change has no better strategy in the new circumstance # the player who did change is now playing with a strictly worse strategy. If these cases are both met, then a player with the small change in their mixed strategy will return immediately to the Nash equilibrium. The equilibrium is said to be stable.
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A proposed mechanism constitutes a Bayesian game (a game of private information), and if it is well-behaved the game has a Bayesian Nash equilibrium. At equilibrium agents choose their reports strategically as a function of type :\hat\theta(\theta) It is difficult to solve for Bayesian equilibria in such a setting because it involves solving for agents' best- response strategies and for the best inference from a possible strategic lie. Thanks to a sweeping result called the revelation principle, no matter the mechanism a designer canIn unusual circumstances some truth-telling games have more equilibria than the Bayesian game they mapped from. See Fudenburg-Tirole Ch. 7.2 for some references.
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Coordination games are games with multiple pure strategy Nash equilibria. There are two general sets of questions that experimental economists typically ask when examining such games: (1) Can laboratory subjects coordinate, or learn to coordinate, on one of multiple equilibria, and if so are there general principles that can help predict which equilibrium is likely to be chosen? (2) Can laboratory subjects coordinate, or learn to coordinate, on the Pareto best equilibrium and if not, are there conditions or mechanisms which would help subjects coordinate on the Pareto best equilibrium? Deductive selection principles are those that allow predictions based on the properties of the game alone.
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In networked systems where competitive decision making takes place, game theory is often used to model system dynamics, and convergence towards equilibria can be considered as a driver of topological evolution. For example, Kasthurirathna and Piraveenan have shown that when individuals in a system display varying levels of rationality, improving the overall system rationality might be an evolutionary reason for the emergence of scale-free networks. They demonstrated this by applying evolutionary pressure on an initially random network which simulates a range of classic games, so that the network converges towards Nash equilibria while being allowed to re-wire. The networks become increasingly scale-free during this process.
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However, the different equilibria are likely to have different distributional implications and may be ranked differently by any given social welfare function. Second, by the Hopf index theorem, in regular economies the number of equilibria will be finite and all of them will be locally unique. This means that comparative statics, or the analysis of how the equilibrium changes when there are shocks to the economy, can still be relevant as long as the shocks are not too large. But this leaves the question of the stability of the equilibrium unanswered, since a comparative statics perspective does not tell us what happens when the market moves away from an equilibrium.
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Figure 3. Reaction correspondence for both players in the Stag Hunt game. Nash equilibria shown with points, where the two player's correspondences agree, i.e. cross Games such as the game of chicken and hawk- dove game in which players score highest when they choose opposite strategies, i.e.
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N. C. Deno, J. J. Jaruzelski, and Alan Schriesheim (1955) "Carbonium ions. I. An acidity function (C0) derived from arylcarbonium ion equilibria." Journal of the American Chemical Society, voume 77, issue 11, pages 3044–3051. Michael E. Jung, Roman Lagoutte, and Ullrich Jahn (2011): "Triphenylcarbenium Tetrafluoroborate".
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Further, games can have both pure strategy and mixed strategy equilibria. An easy example is the pure coordination game, where in addition to the pure strategies (A,A) and (B,B) a mixed equilibrium exists in which both players play either strategy with probability 1/2.
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Joseph W. Greig (1895–1977) was an American geochemist and physical chemist, a pioneer in high temperature phase equilibria and immiscibility investigations of oxides and sulfides. His name has been assigned to a new magnetic mineral, greigite. discovered in 1964. Nine minerals have been named after him.
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IUPAC stipulates that reversible- deactivation polymerization is a kind of chain polymerization, which is propagated by chain carriers that are deactivated reversibly, bringing them into active-dormant equilibria of which there might be more than one. An example of a reversible-deactivation polymerization is group-transfer polymerization.
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His work encompasses equilibria that involve more behavioral adjustments than those defined in orthodox neoclassical models of general equilibrium. According to Buchanan, this approach has major implications for a wide range of issues in economics, such as globalisation, outsourcing, as well as interoccupational and locational mobility.
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In 1956 "Phase Diagrams for Ceramists" was published the first time, containing a collection of phase diagrams.Levin, E.M., McMurdie, H.F., and Hall, F.P., Phase Diagrams for Ceramists: Volume 1, The American Ceramic Society, Columbus, Ohio, p. 6, 1956. This database is known today as "Phase Equilibria Diagrams".
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Macdonell and Mastronardi 2015 provide the first complete characterization of all Nash equilibria to the canonical simplest version of the Colonel Blotto game. This solution, which includes a graphical algorithm for characterizing all the Nash equilibrium strategies, includes previously unidentified Nash equilibrium strategies as well as helps identify what behaviors should never be expected by rational players. Nash equilibrium strategies in this version of the game are a set of bivariate probability distributions: distributions over a set of possible resource allocations for each player, often referred to as Mixed Nash Equilibria (such as can be found in Paper-Rock-Scissors or Matching Pennies as much simpler examples). Macdonell and Mastronardi 2015 solution, proof, and graphical algorithm for identifying Nash equilibria strategies also pertains to generalized versions of the game such as when Colonel Blotto have differing valuations of the battlefields, when their resources have differing effectiveness on the two battlefields (eg one battlefield includes a water landing and Colonel Blotto's resources are Marines instead of Soldiers), and provides insights into versions of the game with three or more battlefields.
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In mathematical optimization, Lemke's algorithm is a procedure for solving linear complementarity problems, and more generally mixed linear complementarity problems. It is named after Carlton E. Lemke. Lemke's algorithm is of pivoting or basis-exchange type. Similar algorithms can compute Nash equilibria for two-person matrix and bimatrix games.
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The Wanzlick equilibrium is a chemical equilibrium between a relatively stable carbene compound and its dimer. The equilibrium was proposed to apply to certain electron-rich alkenes, such as tetraminoethylenes, which have been called "carbene dimers." Such equilibria occur, but the mechanism does not proceed simply, but requires catalysts.
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For example, in work with Marcin Jakubek and Krzysztof Szczygielski,Stark, Oded, Jakubek, Marcin, and Szczygielski, Krzysztof (2018). “Community cohesion and assimilation equilibria.” Journal of Urban Economics 107: 79-88. Stark models the assimilation behavior of a group of migrants who live in a city populated by native inhabitants.
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Eldredge and Stephen Jay Gould proposed punctuated equilibria in 1972. Punctuated equilibrium is a refinement to evolutionary theory. It describes patterns of descent taking place in "fits and starts" separated by long periods of stability. Eldredge went on to develop a hierarchical vision of evolutionary and ecological systems.
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Although there are three Nash equilibria in the Hawk–Dove game, the one which emerges as the evolutionarily stable strategy (ESS) depends upon the existence of any uncorrelated asymmetry in the game (in the sense of anti-coordination games). In order for row players to choose one strategy and column players the other, the players must be able to distinguish which role (column or row player) they have. If no such uncorrelated asymmetry exists then both players must choose the same strategy, and the ESS will be the mixing Nash equilibrium. If there is an uncorrelated asymmetry, then the mixing Nash is not an ESS, but the two pure, role contingent, Nash equilibria are.
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Constantinos Daskalakis was awarded the 2008 ACM Doctoral Dissertation Award for advancing our understanding of behavior in complex networks of interacting individuals, such as those enabled and created by the Internet. His dissertation on the computational complexity of Nash Equilibria provides a novel, algorithmic perspective on game theory and the concept of the Nash equilibrium. For this work Daskalakis was also awarded the 2008 Kalai Prize for outstanding articles at the interface of computer science and game theory, along with Christos Papadimitriou and Paul W. Goldberg. In 2018, Daskalakis was awarded the Nevanlinna Prize for "transforming our understanding of the computational complexity of fundamental problems in markets, auctions, equilibria and other economic structures".
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Berge introduced his original equilibrium notion only in intuitive terms, and the first formal definition of the Berge equilibrium was published by Vladislav Iosifovich Zhukovskii in 1985. The topic of Berge equilibria was then studied in detail by Konstantin Semenovich Vaisman in his 1995 PhD dissertation, and Larbani and Zhukovskii document that the tool became more widely used in the mid-2000s as economists became interested in increasingly complex systems in which players might be more inclined to seek globally favourable equilibria and attach value to other players' payoffs. Colman et al. connect interest in the Berge equilibrium to interest in cooperative game theory, the evolution of cooperation, and topics like altruism in evolutionary game theory.
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All were shown to allow the existence of sunspot equilibria. And, in a suitable twist of intellectual fate, macroeconomists have recently begun to explore the question of whether sunspot expectations can provide a more plausible source of fluctuations in dynamic equilibrium models than the conventional aggregate productivity disturbances. Cass’s third major contribution to economic theory was his work on general equilibrium with incomplete markets, work which grew out of his exploration of the question of existence of sunspot equilibria in models with incomplete asset markets. Cass’s follow-on work on existence and determinacy of general equilibrium in models with incomplete asset markets spawned another large literature which has come to be known simply as GEI.
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The possibility of sunspot equilibria is associated with the existence of multiple equilibria in general equilibrium models. The initial formation by Cass and Shell was constructed in the context of a two period model in which a group of people trade financial contacts in period 1 that depends on the realization of a random variable in period 2. They showed that, if some people are unable to participate in the financial market in period 1, the resulting equilibrium in period 2 can depend on the realization of a random variable that is completely unrelated to economic fundamentals. They call the random variable a sunspot and the resulting allocation is a 'sunspot equilibrium’.
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The study found that caffeine diffusion through the tea leaves is a greatly hindered process.M. Spiro, D. Jaganyi, M.C. Broom, "Kinetics and equilibria of tea infusion. IX: The rates and temperature coefficients of caffeine extraction from green Chun Mee and black Assam Bukial teas", Food chemistry, Vol. 45, No. 5, pp.
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This is very slow computationally. The Frank–Wolfe algorithm improves on this by exploiting dynamic programming properties of the network structure, to find solutions with a faster form of iteration. Creating new and faster algorithms for both selfish and social Wardrop equilibria remains an active research topic in the 2010s.
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Probing Melittin Helix-coil Equilibria in Solutions and Vesicles Hartings, M. R.; Gray, H. B.; Winkler, J. R. J. Phys. Chem. B 2008, 112, 3202-3207. Winkler also participates in the multi-institution NSF Center for Chemical Initiative, a program uniting investigators across multiple disciplines aimed at developing sustainable solar energy.
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There are many Nash equilibria in the Nash demand game. Any x and y such that x + y = z is a Nash equilibrium. If either player increases their demand, both players receive nothing. If either reduces their demand they will receive less than if they had demanded x or y.
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David Cooper and John Kagel have investigated types of learning over similar strategies. Ido Erev and Greg Barron have looked at learning in cognitive strategies. Dale Stahl has characterized learning over decision making rules. Charles A. Holt has studied logit learning in different kinds of games, including games with multiple equilibria.
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She cites Azymuth and João Gilberto as early influences on her musical style. Malheiros's first commercially distributed recording was the title track of Azymuth's 1991 album Curumim, on which she sang lead vocals. Her debut album, Equilibria, was released in 2005. Malheiros wrote or co-wrote nine tracks on the album.
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The Scandinavian Journal of Economics, 3(106), 475-494. Consequently, predictions of the outcome are very sensitive to assumptions made about the bargaining process. The bargaining process can be seen as a game with multiple equilibria. Underinvestment may occur only when the agent fails to coordinate on an efficient equilibrium.
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Lattice programming. Unpublished lectures.) which already uses lattice theory but focuses on cardinal concepts. Milgrom and John Roberts (1994) extended this to comparative statics on equilibria, while Milgrom (1994) demonstrated its wider applicability in comparing optima. Milgrom and Roberts (1996) also generalized Paul Samuelson's application of Le Chatelier's Principle in economics.
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Most DVD-R/+R and some CD-R discs use blue azo dye as the recording layer. phenolic diazo dyes participate in tautomeric equilibria shown here in simplified form (Ar = aryl). Azo dyes are solids. Most are salts, the colored component being the anion usually, although some cationic azo dyes are known.
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Malmberg and collaborators, realized that non-neutral plasmas offer research opportunities not available with neutral plasmas. In contrast to neutral plasmas, plasmas with a single sign of charge can reach states of global thermal equilibria. The possibility of using thermal equilibrium statistical mechanics to describe the plasma provides a large advantage to theory.
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In economics, the theory of contestable markets, associated primarily with its 1982 proponent William J. Baumol, holds that there are markets served by a small number of firms that are nevertheless characterized by competitive equilibria (and therefore desirable welfare outcomes) because of the existence of potential short-term entrants.Brock, 1983. p.1055.
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A signaling system equilibrium A pooling equilibrium A partial pooling equilibrium, dotted lines represent mixed strategies. This game has many Nash equilibria. A few of them stand out where the sender sends a different signal in each state and the receiver takes the appropriate action in every state. Lewis dubbed these signaling systems.
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But Pareto optimality is nowadays considered global by definition.Pareto himself defined it as a local property. Manuale/Manuel Chap III, §22. Thus if the nature of the indifference curves allows non-global optima to arise (as cannot happen if they are convex), then it is possible for equilibria not to be Pareto optimal.
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For uncharged species, the activity coefficient γ0 mostly follows a "salting-out" model: log10 γ0 = bI where I stands for ionic strength. #Assume that the activity coefficients are all equal to 1. This is acceptable when all concentrations are very low. #For equilibria in solution use a medium of high ionic strength.
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Princeton University Press His work with Nobel Laureate Alvin Roth has started a branch of behavioral economics focused on human learning in games and individual choice tasks.Erev, I., & Roth, A. E. (1998). Predicting how people play games: Reinforcement learning in experimental games with unique, mixed strategy equilibria. American economic review, 848-881.
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He is currently interested in the statistical properties of large scales in turbulenceV. Dallas, S. Fauve and A. Alexakis, « Statistical equilibria of large scales in dissipative hydrodynamic turbulence », Phys. Rev. Lett., 115, (2015), p. 204501V. Shukla, S. Fauve and M. Brachet, « Statistical theory of reversals in two-dimensional confined turbulent flows », Phys. Rev.
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Such bodies are hard to visualize, describe or identify. Their form is dissimilar to any typical representative of any other equilibrium geometrical class. They should have minimal "flatness", and, to avoid having two unstable equilibria, must also have minimal "thinness". They are the only non-degenerate objects having simultaneously minimal flatness and thinness.
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Different equilibria emerge as the result of two effects. On the one hand, introducing remote access steals depositors from your competitor because the product specification becomes more appealing (direct effect). On the other hand, banks become closer substitutes (indirect effect). First, banks become closer substitutes as the impact of linear transportation costs decreases.
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This observation is a local instance of a global trend in influenza A coding sequences, where avian, swine, and human strains show different stability. It may be the case that RNA structure is more stable in hosts where the replication temperature is high in order to preserve functional structures or important structural equilibria.
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We have seen that the points of tangency of indifference curves are the Pareto optima, but we also saw previously that the economic equilibria are those points at which indifference curves are tangential to a common price line. It follows that the equilibria are precisely the Pareto optima. This argument applies with one restriction even if the curves are undifferentiable or if the equilibrium is on the boundary. The condition for equilibrium is that no further exchange will take place, and the condition for no further exchange to take place is that there is no direction of motion which benefits one consumer without harming the other; and this is equivalent to the definition of a Pareto optimum.See K. Wicksell, ‘Lectures on Political Economy’ I (1906), Eng. tr.
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The current understanding of ion-pairing equilibria in an aqueous environment can also be traced to the Eigen-Tamm model that introduced the use of two equlibria states for ion pairs: the contact ion pair (CIP) and the separated ion pair (SIP). As an early application of ion-pairing equilibria, Kester and Pytkowicz studied the role of sulfate and divalent cation ion-pairing in seawater. This ion- specific behavior was also elucidated through Collin's Law of Matching Water Affinities that describes the strength of ion-pairing in terms of ion size and counterion, while also incorporating coordination state and entropy. Modern computational approaches to simulation of ion-pairing involve molecular dynamic simulations and ab initio calculations that often incorporate polarizable continuum solvent models.
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Nash Equilibria for when the Citizen has no Credible Exit Threat (E < 0). Notice that it does not matter whether the Government is Dependent or Autonomous (L can take any value). The EVL game is solved differently whether the Government is dependent or autonomous from the Citizen, whether the Citizen has or does not have a credible Exit option, and the cost of using Voice. Nash Equilibria for an Autonomous Government (L < 1) and a Citizen with no Credible Exit Threat (E < 0) EVL shows that the only time a Government will Respond to the Citizen using their Voice is when the Government is dependent on the support of the Citizen (L > 1) and when the Citizen has a credible Exit option (E > 0).
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This observation took on a life of its own as what Shell called the Philadelphia Pholk theorem: if the first welfare theorem doesn't hold, then you can find an economy where sunspots matter. In addition to raising troubling questions about what the right state space was for dynamic stochastic economies, the notion of sunspot equilibrium raised a number of deep questions about the overall determinacy of economic equilibria and the role of the welfare theorems in the occurrence or non-occurrence of sunspot equilibria. These questions spawned a large literature on determinacy in dynamic economies in which the welfare theorems broke down. These include overlapping generations models, growth models with externalities or taxes, and models in which asset markets were incomplete.
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Pre-pub PDF. In contrast to other standard modeling methods, ACE events are driven solely by initial conditions, whether or not equilibria exist or are computationally tractable. ACE modeling, however, includes agent adaptation, autonomy, and learning.Tesfatsion, Leigh (2006), "Agent-Based Computational Economics: A Constructive Approach to Economic Theory", ch. 16, Handbook of Computational Economics, v.
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Like other refinements of Nash equilibriumGovindan, Srihari & Robert Wilson, 2008. "Refinements of Nash Equilibrium," The New Palgrave Dictionary of Economics, 2nd edition. used in game theory stability selects subsets of the set of Nash equilibria that have desirable properties. Stability invokes stronger criteria than other refinements, and thereby ensures that more desirable properties are satisfied.
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This research usually focuses on particular sets of strategies known as "solution concepts" or "equilibria". A common assumption is that players act rationally. In non-cooperative games, the most famous of these is the Nash equilibrium. A set of strategies is a Nash equilibrium if each represents a best response to the other strategies.
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In biology thiyl radicals are responsible for the formation of the deoxyribonucleic acids, building blocks for DNA. This conversion is catalysed by ribonucleotide reductase (see figure). Thiyl intermediates also are produced by the oxidation of glutathione, an antioxidant in biology. Thiyl radicals (sulfur-centred) can transform to carbon-centred radicals via hydrogen atom exchange equilibria.
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The molecular environment around a supramolecular system is also of prime importance to its operation and stability. Many solvents have strong hydrogen bonding, electrostatic, and charge-transfer capabilities, and are therefore able to become involved in complex equilibria with the system, even breaking complexes completely. For this reason, the choice of solvent can be critical.
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A generalization of backward induction is subgame perfection. Backward induction assumes that all future play will be rational. In subgame perfect equilibria, play in every subgame is rational (specifically a Nash equilibrium). Backward induction can only be used in terminating (finite) games of definite length and cannot be applied to games with imperfect information.
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They do not do that in proportion when optimization drives > model solutions. However, we know that many-agent models can have multiple > equilibria when all agents optimize. There may be fruitful paths forward in > that direction. Old contributions should best be left buried when they > involve using capital as a stick to beat marginal theory.
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PC-SAFT is an equation of state that is based on statistical associating fluid theory (SAFT). Like other SAFT equations of state, it makes use of statistical mechanical methods (in particular perturbation theory).Chapman, Walter G., et al. "SAFT: Equation-of-state solution model for associating fluids." Fluid Phase Equilibria 52 (1989): 31-38.
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Inductive selection principles are those that allow predictions based on characterizations of dynamics. Under some conditions at least groups of experimental subjects can coordinate even complex non-obvious asymmetric Pareto-best equilibria. This is even though all subjects decide simultaneously and independently without communication. The way by which this happens is not yet fully understood.
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In the case of a tie, each player receives v_i / 2 utility. Time is valuable, each player uses one unit of utility per period of time. This formulation is slightly more complex since it allows each player to assign a different value to the object. Its equilibria are not as obvious as the other formulation.
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The possible equilibria between bodies are determined by the physical properties of the walls that separate the bodies. Equilibrium thermodynamics in general does not measure time. Equilibrium thermodynamics is a relatively simple and well settled subject. One reason for this is the existence of a well defined physical quantity called 'the entropy of a body'.
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Sodium dithionite is a reducing agent. At pH=7, the potential is -0.66 V vs NHE. Redox occurs with formation of sulfite: :S2O42- \+ 2 H2O → 2 HSO3− \+ 2 e− \+ 2 H+ Sodium dithionite reacts with oxygen: :Na2S2O4 \+ O2 \+ H2O → NaHSO4 \+ NaHSO3 These reactions exhibit complex pH-dependent equilibria involving bisulfite, thiosulfate, and sulfur dioxide.
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This is a stable equilibrium. The response to a small perturbation is forces that tend to restore the equilibrium. If more than one stable equilibrium state is possible for a system, any equilibria whose potential energy is higher than the absolute minimum represent metastable states. Diagram of a ball placed in a neutral equilibrium.
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Most computational modeling research describes systems in equilibrium or as moving between equilibria. Agent-based modeling, however, using simple rules, can result in different sorts of complex and interesting behavior. The three ideas central to agent-based models are agents as objects, emergence, and complexity. Agent- based models consist of dynamically interacting rule-based agents.
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As that continuum shrinks to zero, the players strategies converge to the predicted Nash equilibria of the original, unperturbed, complete information game. The result is also an important aspect of modern-day inquiries in evolutionary game theory where the perturbed values are interpreted as distributions over types of players randomly paired in a population to play games.
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In this interval, the government finds it optimal to repay old debt if it can sell new debt, and it's optimal to default if it cannot sell new debt. In this model setup, the essence of self-fulfilling crisis is highlighted: market sentiment will justify itself, and the existence of multiple equilibria and sunspot variable are the key.
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In 1911 he was appointed director of the school of engineering in Bologna. Canevazzi's research dealt with molecular equilibria in static mechanics, applications of the Menabrea theorem in elasticity, and studies of reinforced concrete. He developed a new method of calculating static stresses for buildings in earthquake zones. His method influenced building codes for earthquake resistance.
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Robert Minard Garrels (August 24, 1916 – March 8, 1988) was an American geochemist. Garrels applied experimental physical chemistry data and techniques to geology and geochemistry problems. The book Solutions, Minerals, and Equilibria co-authored in 1965 by Garrels and Charles L. Christ revolutionized aqueous geochemistry. Garrels earned a bachelor's degree in geology from The University of Michigan in 1937.
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While (Hare, Hare) remains a Nash equilibrium, it is no longer risk dominant. Nonetheless many would call this game a stag hunt. 100px In addition to the pure strategy Nash equilibria there is one mixed strategy Nash equilibrium. This equilibrium depends on the payoffs, but the risk dominance condition places a bound on the mixed strategy Nash equilibrium.
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63 for details Redox equilibria play an important role in the electron transport chain. The various cytochromes in the chain have different standard redox potentials, each one adapted for a specific redox reaction. This allows, for example, atmospheric oxygen to be reduced in photosynthesis. A distinct family of cytochromes, the cytochrome P450 oxidases, are involved in steroidogenesis and detoxification.
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Powell was educated at Durham University where he was awarded a Bachelor of Science degree in 1970. He went on to study at the University of Oxford where he was awarded a Doctor of Philosophy degree in 1973 for research on mineral equilibria in the schist rock near Fort William, Scotland supervised by Stephen W. Richardson.
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Membranes can also be used to separate ethanol and water. Membrane-based separations are not subject to the limitations of the water-ethanol azeotrope because the separations are not based on vapor-liquid equilibria. Membranes are often used in the so-called hybrid membrane distillation process. This process uses a pre-concentration distillation column as first separating step.
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337 In 1972 Niles Eldredge and Stephen Jay Gould used fossil evidence to advocate the theory of punctuated equilibrium, which maintains that evolution is characterized by long periods of relative stasis and much shorter periods of relatively rapid change.Eldredge, Niles and S. J. Gould (1972). "Punctuated equilibria: an alternative to phyletic gradualism" In T.J.M. Schopf, ed., Models in Paleobiology.
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This paper by Cuff and John Burbridge examines capital tax competition in different regions through a comparison of Nash equilibria using variations of the standard capital tax model. The conclusion finds that inefficiencies in both capital and head taxes can be attributed to regions' incentives to manipulate the terms of trade, rather than any difference in increasing returns.
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This graph illustrates the stable equilibria for cyclin-B1/CDK1 activity at varying cyclin B1 concentrations, with the threshold of cyclin B concentration for entering mitosis higher than the threshold for exiting mitosis. These positive feedback loops encode a hysteretic bistable switch in CDK1 activity relative to cyclin B1 levels (see figure). This switch is characterized by two distinct stable equilibria over a bistable region of cyclin B1 concentrations. One equilibrium corresponds to interphase and is characterized by inactivity of Cyclin-B1/CDK1 and Cdc25, and a high level of Wee1 and Myt1 activity. The other equilibrium corresponds to M-phase and is characterized by high activity of Cyclin-B1/CDK1 and Cdc25, and low Wee1 and Myt1 activity. Within the range of bistability, a cell’s state depends upon whether it was previously in interphase or M-phase: the threshold concentration for entering M-phase is higher than the minimum concentration that will sustain M-phase activity once a cell has already exited interphase. Scientists have both theoretically and empirically validated the bistable nature of the G2/M transition. The Novak-Tyson model shows that the differential equations modelling the cyclin-B/CDK1-cdc25-Wee1-Myt1 feedback loop admit two stable equilibria over a range of cyclin-B concentrations.
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Seawater pH is typically limited to a range between 7.5 and 8.4. However, there is no universally accepted reference pH-scale for seawater and the difference between measurements based on different reference scales may be up to 0.14 units.Stumm, W, Morgan, J. J. (1981) Aquatic Chemistry, An Introduction Emphasizing Chemical Equilibria in Natural Waters. John Wiley & Sons. pp. 414–416. .
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His research activities include the processing science of materials with emphasis on bio-inspired methods of self-assembly, thermodynamics and phase equilibria, diffusion and structural studies in ionic systems. His most recent work on functionalized graphene produced through thermal reduction of graphene oxide demonstrated many advantages in technologies ranging from nanocomposites to electrochemical devices for chemical sensing, energy harvesting, and energy storage.
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The algorithm can find at most n + m different Nash equilibria. Any choice of initially-dropped label determines the equilibrium that is eventually found by the algorithm. The Lemke–Howson algorithm is equivalent to the following homotopy-based approach. Modify G by selecting an arbitrary pure strategy g, and giving the player who owns that strategy, a large payment B to play it.
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There are many combinations of consumer utility, production mixes, and factor input combinations consistent with efficiency. In fact, there are an infinity of consumption and production equilibria that yield Pareto optimal results. There are as many optima as there are points on the aggregate production–possibility frontier. Hence, Pareto efficiency is a necessary, but not a sufficient condition for social welfare.
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Neither trader alone can run out the government's reserves, but both can if they sell together. The payoff matrix of the two traders is given below. There are two Nash equilibria in this game. In the first (good) equilibrium, if neither trader believes the other will attack, the Nash equilibrium in the northwest corner is realized and the fixed exchange rate survives.
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Mertens stability is a solution concept used to predict the outcome of a non- cooperative game. A tentative definition of stability was proposed by Elon Kohlberg and Jean-François Mertens for games with finite numbers of players and strategies. Later, MertensMertens, Jean-François, 1989, and 1991. "Stable Equilibria - A Reformulation," Mathematics of Operations Research, 14: 575-625 and 16: 694-753.
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Equilibria are not always Pareto efficient, and a number of game theorists design ways to enforce Pareto efficient play, or play that satisfies some other sort of social optimality. The theory of this is called implementation theory. Other economists seek to design games based on a certain set of outcomes, an effort which goes under the name of mechanism design.
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Reny, P., and S. Zamir (2004) "On the Existence of Pure Strategy Monotone Equilibria in Asymmetric First-Price Auctions," Econometrica, Vol. 72 No. 4, pp. 1105–1125. The first formal analysis of auctions was by William Vickrey (1961). Vickrey considers two buyers bidding for a single item. Each buyer's value, v, is an independent draw from a uniform distribution with support [0,1].
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In Diamond's model producers are more likely to produce if they see others producing. The increase in possible trading partners increases the likelihood of a given producer finding someone to trade with. As in other cases of coordination failure, Diamond's model has multiple equilibria, and the welfare of one agent is dependent on the decisions of others.Cooper and John (1988), pages 452-3.
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Activity coefficients can be used to predict simple phase equilibria (vapour–liquid, liquid–liquid, solid–liquid), or to estimate other physical properties (e.g. viscosity of mixtures). Models such as UNIQUAC allow chemical engineers to predict the phase behavior of multicomponent chemical mixtures. They are commonly used in process simulation programs to calculate the mass balance in and around separation units.
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An AMOC shutdown would be fuelled by two positive feedbacks, the accumulation of both freshwater and heat in areas on downwelling. AMOC exports freshwater from the North Atlantic, and a reduction in overturning would freshen waters and inhibit downwelling.Dijkstra, Henk A. "Characterization of the multiple equilibria regime in a global ocean model." Tellus A: Dynamic Meteorology and Oceanography 59.5 (2007): 695–705.
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The First Fundamental Welfare Theorem asserts that market equilibria are Pareto efficient. In a pure exchange economy, a sufficient condition for the first welfare theorem to hold is that preferences be locally nonsatiated. The first welfare theorem also holds for economies with production regardless of the properties of the production function. Implicitly, the theorem assumes complete markets and perfect information.
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Research building on the Arrow–Debreu–McKenzie model has revealed some problems with the model. The Sonnenschein–Mantel–Debreu results show that, essentially, any restrictions on the shape of excess demand functions are stringent. Some think this implies that the Arrow–Debreu model lacks empirical content. At any rate, Arrow–Debreu–McKenzie equilibria cannot be expected to be unique, or stable.
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The data determining Arrow-Debreu equilibria include initial endowments of capital goods. If production and trade occur out of equilibrium, these endowments will be changed further complicating the picture. > In a real economy, however, trading, as well as production and consumption, > goes on out of equilibrium. It follows that, in the course of convergence to > equilibrium (assuming that occurs), endowments change.
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The notion of conjectures has maintained a long history in the Industrial Organization theory ever since the introduction of Conjectural Variations Equilibria by Arthur Bowley in 1924Bowley, A. L. (1924). The Mathematical Groundwork of Economics, Oxford University Press. and Ragnar Frisch (1933)Frisch R. 1951 [1933]. Monopoly – Polypoly – The concept of force in the economy, International Economic Papers, 1, 23–36.
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A signaling game is the simplest kind of a dynamic Bayesian game. There are two players, one of them (the "receiver") has only one possible type, and the other (the "sender") has several possible types. The sender plays first, then the receiver. To calculate a PBE in a signaling game, we consider two kinds of equilibria: a separating equilibrium and a pooling equilibrium.
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He is also known for his contribution to game theory. In 1964 Lemke (with J. T. Howson) constructed an algorithm for finding Nash equilibria the case of finite two-person games. For this work Lemke received in 1978 the John von Neumann Theory Prize. He was elected to the 2002 class of Fellows of the Institute for Operations Research and the Management Sciences.
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The ASD network led by Burns developed a complex of interrelated theories. Besides the ASD theory core, Burns and several of his collaborators developed a socially embedded, role based game theory, generalized game theory, which recognizes the social and psychological complexity of human motivation and action, the dilemmas and contradictions often facing social agents, and the problems matters of game equilibria and disequilibria.
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The 16-electron alkyl complex undergoes migratory insertion of a CO to form the coordinately unsaturated acyl. This species once again gives an 18-electron acyl complex.R. V. Kastrup, J. S. Merola, A. A. Oswald; P-31 NMR Studies of Equilibria and Ligand Exchange in Triphenylphosphine Rhodium Complex and Related Chelated Bisphosphine Rhodium Complex Hydroformylation Catalyst Systems. J. Am. Chem. Soc. 1982.44-16. .
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This is an instance of coordination failure in the presence of indivisibility. Obviously, there can also be cases where but . This is an instance where the two viable institutional arrangements cannot be Pareto ranked. Agents exhibit conflicting interests in the two equilibria and the emergence of one institutional arrangement as opposed to the other may depend on the distribution of decisional power.
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Monthly Review Press, New York who have stressed the opposite direction of causation. The complementarities existing in the different organizational equilibria integrate both directions of causation in a single analytical framework. A similar approach has been used to explain organizational diversity in knowledge-intensive industries, such as software.Landini F (2012) Technology, property rights and organizational diversity in the software industry.
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As a chemist he discovered phosphorus sesquisulfide, a compound that will later be used in the manufacture of matches. He continued research on the allotropic transformation of phosphorus, and was also the author of works on chemical equilibria. In 1899 he became a member of the Académie des sciences (chemistry section), of which in 1921, he was named its president.
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PSRK (short for Predictive Soave–Redlich–Kwong)Holderbaum T., “Die Vorausberechnung von Dampf-Flüssig-Gleichgewichten mit einer Gruppenbeitragszustandsgleichung”, Fortschrittsber. VDI Reihe 3, 243, 1–154, 1991. is an estimation method for the calculation of phase equilibria of mixtures of chemical components. The original goal for the development of this method was to enable the estimation of properties of mixtures containing supercritical components.
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The Berge equilibrium has been motivated as the exact opposite of a Nash equilibrium, in that while the Nash equilibrium models selfish behaviours, the Berge equilibrium models altruistic behaviours. Moussa Larbani and Vladislav Iosifovich Zhukovskii note that Berge equilibria could be interpreted as a method for formalising the Golden Rule in strategic interactions. One advantage of the Berge equilibrium over the Nash equilibrium is that the Berge results may agree more closely with results obtained from experimental psychology and experimental economics. Several authors have noted that players asked to play games like the Prisoner's Dilemma or the ultimatum game in laboratory scenarios rarely reach the Nash Equilibrium result, in part because people in real situations often do attach value to the well-being of others, and that therefore Berge equilibria could sometimes be a better fit to real behaviour in certain situations.
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A major difference to the standard Ramsey growth model was that Cass considered the case where consumption in future periods is discounted, thus implicitly assuming that consumers prefer consumption today to consumption tomorrow. This modified version of the Ramsey growth model is also known as the Ramsey-Cass-Koopmans model, named after Frank Ramsey, David Cass and Tjalling Koopmans. He was also famous for the "Cass criterion" for overlapping generations models and in the neoclassical growth model, and his work, together with Karl Shell, on the influence of extrinsic uncertainty on economic equilibria, also known as the concept of sunspot equilibria or the theory of sunspots. Together with Joseph Stiglitz he proved conditions under which it is possible for an investor to achieve an optimal portfolio under the restriction of being able to buy only two mutual funds.
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Over the years he has taught a variety of undergraduate and graduate level courses in materials, ranging from introductory classes to courses in phase equilibria, optical materials, phase transformations, thermodynamics and composites. He currently teaches seminars on “Glass” and “Materials, Energy and Society” at the undergraduate Freshman level, and the required course on “Fundamentals of Heat Transfer” course for students studying Mechanical Engineering at Harvard University.
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In introducing the Arrow–Debreu model in 1954, they proved the existence (but not the uniqueness) of an equilibrium and also proved that every Walras equilibrium is Pareto efficient; in general, equilibria need not be unique. • In their models, the ("primal") vector space represented quantities while the "dual" vector space represented prices.Kantorovich, Leonid, and Victor Polterovich (2008). "Functional analysis", in S. Durlauf and L. Blume, ed.
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They often form dimers, unlike their boron analogues, but this tendency diminishes for branched-chain alkyls (e.g. Pri, Bui, Me3CCH2); for example, triisobutylaluminium exists as an equilibrium mixture of the monomer and dimer.Greenwood and Earnshaw, pp. 257–67Martin B. Smith, Journal of Organometallic Chemistry, The Monomer-Dimer Equilibria of Liquid Ammonium Alkyls II Triisobutylaluminum Journal of Organometallic Chemistry, Volume 22, Issue 2, April 1970, Pages 273-281.
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In this case unstable equilibria are very unlikely to arise in practice, since any minute change in the proportions of each strategy seen will lead to a change in strategy and the breakdown of the equilibrium. The Nash equilibrium defines stability only in terms of unilateral deviations. In cooperative games such a concept is not convincing enough. Strong Nash equilibrium allows for deviations by every conceivable coalition.
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The results of their study confirmed the existence of multiple equilibria; one near the targeted inflation rate as was previously identified; as well as a second equilibrium with zero nominal interest rates and low inflation to mild deflation. This research has taken on importance in the post financial crisis discourse regarding the presence of a liquidity trap and the subsequent historically low interest rates.
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The Dortmund Data Bank was founded in the 1970s at the University of Dortmund in Germany. The original reason for starting a vapor–liquid phase equilibria data collection was the developmentGmehling J., Weidlich U., "Die Dortmunder Datenbank. Basis für die Weiterentwicklung der UNIFAC-Methode", Chem.Ing.Tech., 57(5), 447-449, 1985 of the group contribution method UNIFAC which allows to estimate vapor pressures of mixtures.
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Walras also proposed a dynamic process by which general equilibrium might be reached, that of the tâtonnement or groping process. The tâtonnement process is a model for investigating stability of equilibria. Prices are announced (perhaps by an "auctioneer"), and agents state how much of each good they would like to offer (supply) or purchase (demand). No transactions and no production take place at disequilibrium prices.
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Starch, simple sugars, oxalic acid, and some amino acids tend to increase the rate of absorption of chromium(III). This is a result of ligand chelation, converting hexaaqua Cr3+ into more lipophilic forms. In contrast, calcium, magnesium, titanium, zinc, vanadium, and iron reduce the rate of absorption. Presumably, these ions introduce new metal- ligand equilibria, thus decreasing the lipophilic ligand pool available to Cr3+.
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A pooling equilibrium in game theory is an equilibria result of a signaling game. In a signaling game, players send actions called "signals" to other players in the game. Signaling actions are chosen based on privately held information (not known by other players in the game). These actions do not reveal a player's "type" to other players in the game, and other players will choose strategies accordingly.
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The Walrasian equilibria of an exchange economy in a general equilibrium model, will lie in the core of the cooperation game between the agents. Graphically, and in a two-agent economy (see Edgeworth Box), the core is the set of points on the contract curve (the set of Pareto optimal allocations) lying between each of the agents' indifference curves defined at the initial endowments.
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Heterocyclic analogs of cyclohexane are pervasive in sugars, piperidines, dioxanes, etc. They exist generally follow the trends seen for cyclohexane, i.e. the chair conformer being most stable. The axial- equatorial equilibria (A values) are however strongly affected by the replacement of a methylene by O or NH. Illustrative are the conformations of the glucosides. 1,2,4,5-Tetrathiane ((SCH2)3) lacks the unfavorable 1,3-diaxial interactions of cyclohexane.
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Typically, shallow lakes are in one of two contrasting alternative stable states:Scheffer M, 1993. Alternative equilibria in shallow lakes. Trends in Ecology & Evolution 8: 275–-279 a clear state with submerged macrophytes and piscivorous fish, or a turbid state dominated by phytoplankton and benthivorous fish. A switch from one state to the other is largely driven by the input of nutrients (phosphorus and nitrogen) to the ecosystem.
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Many transition-metal compounds violate this rule due to the formation of complex ions, a scenario not part of the equilibria that are involved in simple precipitation of salts from ionic solution. For example, copper(I) chloride is insoluble in water, but it dissolves when chloride ions are added, such as when hydrochloric acid is added. This is due to the formation of soluble CuCl2− complex ions.
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Nash Equilibria for a Dependent Government (L > 1) and a Citizen with a Credible Exit Threat (E > 1). This is the only case where the Government chooses to Respond. In EVL, if the Government is dependent on the Loyalty of the Citizen then L > 1 and if the Government is autonomous, i.e. not dependent on the loyalty and support of the Citizen, L < 1.
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When significant evolutionary change occurs, the theory proposes that it is generally restricted to rare and geologically rapid events of branching speciation called cladogenesis. Cladogenesis is the process by which a species splits into two distinct species, rather than one species gradually transforming into another.Gould, Stephen Jay, & Eldredge, Niles (1977). "Punctuated equilibria: the tempo and mode of evolution reconsidered." Paleobiology 3 (2): 115-151. (p.
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For this reason it is necessary to confirm the consistency of the obtained parameters in the whole range of compositions (including binary subsystems, experimental and calculated lie-lines, Hessian matrix, etc.).Li, Z.; Smith, K. H.; Mumford, K. A.; Wang, Y.; Stevens, G. W., Regression of NRTL parameters from ternary liquid–liquid equilibria using particle swarm optimization and discussions. Fluid Phase Equilib. 2015, 398, 36-45.
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The titration process creates solutions with compositions ranging from pure acid to pure base. Identifying the pH associated with any stage in the titration process is relatively simple for monoprotic acids and bases. The presence of more than one acid or base group complicates these computations. Graphical methods, such as the equiligraph, have long been used to account for the interaction of coupled equilibria.
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Other researchers further generalize Rabin (1993)'s model by studying repeated interactions in N-person extensive form games, and also by including inequity aversion into agent's preference. Charness and Rabin also augmented their quasi-maximin preference with reciprocity concern. However, this type of reciprocity models usually has multiple equilibria and suffers from model complexity, which makes it hard to empirically test for the model.
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The classical results due to Edelman, Ostrovsky and Schwarz and Varian hold in the full information setting – when there is no uncertainty involved. Recent results as Gomes and Sweeney R. D. Gomes and K. S. Sweeney. "Bayes–Nash equilibria of the generalized second price auction". In EC ’09: Proceedings of the tenth ACM conference on Electronic commerce, pages 107–108, New York, NY, USA, 2009.
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The Favorskii reaction is an alternative set of reaction conditions, which involves prereaction of the acetylene with an alkali metal hydroxide such as KOH. The reaction proceeds through equilibria, making the reaction reversible: # HC≡CH + KOH HC≡CK + H2O # RR'C=O + HC≡CK RR'C(OK)C≡CH To overcome this reversibility, the reaction often uses an excess of base to trap the water as hydrates.
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The titration process creates solutions with compositions ranging from pure acid to pure base. Identifying the pH associated with any stage in the titration process is relatively simple for monoprotic acids and bases. The presence of more than one acid or base group complicates these computations. Graphical methods, such as the equiligraph, have long been used to account for the interaction of coupled equilibria.
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This process continues until one reaches the first move of the game. The strategies which remain are the set of all subgame perfect equilibria for finite-horizon extensive games of perfect information. However, backward induction cannot be applied to games of imperfect or incomplete information because this entails cutting through non-singleton information sets. A subgame perfect equilibrium necessarily satisfies the one-shot deviation principle.
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He worked ten years for the Institute of Cellulose Research of the . Challa obtained his title of doctor in maths and physics on 13 May 1959 under Jan Ketelaar at the University of Amsterdam. His thesis was titled: "Formation of polyethylene terephthalate by ester interchange : equilibria kinetics and molecular weight distribution". After starting as professor at the University of Groningen he set the possibility to study polymer chemistry.
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A reactive liquid extraction process is a liquid-liquid extraction process that is intensified through a mechanism involving a reversible reaction between the extracted chemical species and a host chemical species constituting, or present in, the extractant.Tamada, J. A.; Kertes, A. S.; King, C. J. “Extraction of carboxylic acids with amine extractants. 1. equilibria and law of mass action modeling”. Ind. Eng. Chem. Res. 29, pages 1319-1326, 1990.
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The Brouwer fixed point theorem is a fundamental result in topology which proves the existence of fixed points for continuous functions defined on compact, convex subsets of Euclidean spaces. Kakutani's theorem extends this to set-valued functions. The theorem was developed by Shizuo Kakutani in 1941, and was used by John Nash in his description of Nash equilibria. It has subsequently found widespread application in game theory and economics.
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In 1965, Reinhard Selten introduced his solution concept of subgame perfect equilibria, which further refined the Nash equilibrium. Later he would introduce trembling hand perfection as well. In 1994 Nash, Selten and Harsanyi became Economics Nobel Laureates for their contributions to economic game theory. In the 1970s, game theory was extensively applied in biology, largely as a result of the work of John Maynard Smith and his evolutionarily stable strategy.
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Systems in mutual thermodynamic equilibrium are simultaneously in mutual thermal, mechanical, chemical, and radiative equilibria. Systems can be in one kind of mutual equilibrium, though not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by a thermodynamic operation. In a macroscopic equilibrium, perfectly or almost perfectly balanced microscopic exchanges occur; this is the physical explanation of the notion of macroscopic equilibrium.
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Alternatively, the model can be portrayed in game theoretic terms as initially a game with multiple Nash equilibria, with government having the capability of affecting the payoffs to switch to a game with just one equilibrium. Although it is possible for the national government to increase a country's welfare in the model through export subsidies, the policy is of beggar thy neighbor type.Cohen and Lipson, p. 22.Baldwin, p. 69.
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Formally, a stag hunt is a game with two pure strategy Nash equilibria—one that is risk dominant and another that is payoff dominant. The payoff matrix in Figure 1 illustrates a generic stag hunt, where a>b\ge d>c. Often, games with a similar structure but without a risk dominant Nash equilibrium are called assurance games. For instance if a=2, b=1, c=0, and d=1.
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A chlorine- hydrogen reaction is also explosive, but only in the presence of light and heat. A bromine-hydrogen reaction is even less explosive; it is explosive only when exposed to flames. Iodine and astatine only partially react with hydrogen, forming equilibria. All halogens form binary compounds with hydrogen known as the hydrogen halides: hydrogen fluoride (HF), hydrogen chloride (HCl), hydrogen bromide (HBr), hydrogen iodide (HI), and hydrogen astatide (HAt).
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She is the Director of Centre for Process Systems Engineering at Imperial College London and is the Co-Director of the Institute of Molecular Science and Engineering at Imperial College London. In 2015 she was elected to the Royal Academy of Engineering. In 2016 she was elected to the Royal Society of Chemistry. She is on the editorial board of the journals Molecular Systems Design & Engineering and Fluid Phase Equilibria.
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Saddle azeotrope calculated with UNIFAC at 1 atm. Red lines are vapor compositions and blue lines are liquid compositions. Image is rotating to more clearly show the saddle-like shape of the vapor–liquid equilibria The UNIFAC method (UNIQUAC Functional-group Activity Coefficients)Aage Fredenslund, Russell L. Jones and John M. Prausnitz, "Group-Contribution Estimation of Activity Coefficients in Nonideal Liquid Mixtures", AIChE Journal, vol. 21 (1975), p.
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Equilibrium chemistry is concerned with systems in chemical equilibrium. The unifying principle is that the free energy of a system at equilibrium is the minimum possible, so that the slope of the free energy with respect to the reaction coordinate is zero. This principle, applied to mixtures at equilibrium provides a definition of an equilibrium constant. Applications include acid–base, host–guest, metal–complex, solubility, partition, chromatography and redox equilibria.
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Metallacarboxylic acids exist in equilibria with the carboxylate anions, LnMCO2−. Metallacarboxylate esters (LnMCO2R) arise by the addition of alkoxide to metal carbonyl: :[LnM-CO]+ \+ ROH → [LnM-CO2R] + H+ Metallacarboxylic amides (LnMC(O)NR2) arise by the addition of amide to metal carbonyl: :[LnM-CO]+ \+ 2 RNH2 → [LnM-C(O)N(H)R] + RNH3+ Derivatives of metalladithiacarboxylic acids are also known. They are prepared by treating anionic complexes with carbon disulfide.
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For the equations of the law of mass action the reciprocal relations appear in the linear approximation near equilibrium as a consequence of the detailed balance conditions. According to the reciprocal relations, the damped oscillations in homogeneous closed systems near thermodynamic equilibria are impossible because the spectrum of symmetric operators is real. Therefore, the relaxation to equilibrium in such a system is monotone if it is sufficiently close to the equilibrium.
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For the case n=2, this problem was independently proposed by János Bolyai and Nikolai Lobachevsky, the founders of hyperbolic geometry. But though many papers were written on this subject, the equations of motion for any number, n, of bodies were obtained only in 2008.F. Diacu, E. Pérez-Chavela and M. Santoprete, The n-body problem in spaces of constant curvature. Part I: Relative equilibria, J. Nonlinear Sci.
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However, this effect would be tempered by a concomitant reduction in warm water transport to the North Atlantic under a weakened AMOC, a negative feedback on the system. As well as paleoceanographic reconstruction, the mechanism and likelihood of collapse has been investigated using climate models. Earth Models of Intermediate Complexity (EMICs) have historically predicted a modern AMOC to have multiple equilibria, characterised as warm, cold and shutdown modes.Rahmstorf, S. (2002).
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Scarf received the 1973 Frederick W. Lanchester Award for his contribution The Computation of Economic Equilibria with the collaboration of Terje Hansen, which pioneered the use of numeric algorithms to solve general equilibrium systems using Applied general equilibrium models. He was a member of the American Academy of Arts and Sciences, and was elected to the 2002 class of Fellows of the Institute for Operations Research and the Management Sciences.
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On the other hand, if the total number of molecules exceeds Np, the only possible equilibrium state is the one described above, with one balloon on the left of the peak and one on the right. Equilibria in which both balloons are on the right of the pressure peak also exist but are unstable. This is easy to verify by squeezing the air back and forth between two interconnected balloons.
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By contrast, in Keynes' formulation, p=1 and there are many possible Nash equilibria. In play of the p-beauty contest game (where p differs from 1), players exhibit distinct, boundedly rational levels of reasoning as first documented in an experimental test by Nagel (1995). The lowest, "Level 0" players, choose numbers randomly from the interval [0,100]. The next higher, "Level 1" players believe that all other players are Level 0.
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As mentioned, imperfect information in a leadership game reduces to Cournot competition. However, some Cournot strategy profiles are sustained as Nash equilibria but can be eliminated as incredible threats (as described above) by applying the solution concept of subgame perfection. Indeed, it is the very thing that makes a Cournot strategy profile a Nash equilibrium in a Stackelberg game that prevents it from being subgame perfect. Consider a Stackelberg game (i.e.
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A separating equilibrium describes one type of perfect Bayesian equilibria that may arise in signaling games. The simplest example of such signaling games involves two players, who each take an action in sequence. The first player is privately informed with some payoff-relevant information, which is unavailable to the second player. After the first player acts, the second player chooses an action after observing the first player's action.
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Apart from this similarity, the theories differ significantly from each other in the mechanisms underlying transformation. However, this difference does not lie in the struggle for survival and survival of the fittest, but in the way in which natural selection is integrated with variability, competition and environmental conditions. Transmutation is a convergent result of structurally different mechanisms. The similarity of Matthew's scheme to the theory of punctuated equilibria is equally superficial.
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Equilibria are defined for specific crystal phases. Therefore, the solubility product is expected to be different depending on the phase of the solid. For example, aragonite and calcite will have different solubility products even though they have both the same chemical identity (calcium carbonate). Under any given conditions one phase will be thermodynamically more stable than the other; therefore, this phase will form when thermodynamic equilibrium is established.
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Paul W. Chun is a professor emeritus at the University of Florida. He is a researcher in the field of protein folding equilibria, in particular, he is known as the "leading proponent" of using the Planck-Benzinger thermal work function to understand protein folding thermodynamics and stability. As such Chun has written a number of papers relating to the thermodynamics of protein folding.Faculty profile at the University of Florida .
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They reproduce and are subject to the forces of natural selection, with the payoffs of the game representing reproductive success (biological fitness). It is imagined that alternative strategies of the game occasionally occur, via a process like mutation. To be an ESS, a strategy must be resistant to these alternatives. Given the radically different motivating assumptions, it may come as a surprise that ESSes and Nash equilibria often coincide.
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A similar derivation may be found in José & Saletan, Classical Dynamics: A Contemporary Approach, pgs. 31-33 The original two-variable problem has been reduced to a one-variable problem. For many applications the effective potential can be treated exactly like the potential energy of a one-dimensional system: for instance, an energy diagram using the effective potential determines turning points and locations of stable and unstable equilibria.
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Unilateral market power is one of the most common causes of prices being higher than the competitive equilibrium. Market power has been seen to exert more upward pressure on prices than do variations in the quantity of sellers present in the market. This is due to effects relating to Nash equilibria and profitable deviations that can be made by raising prices.Davis D.D. (2008) Market Power and Collusion in Laboratory Markets.
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In the IS-LM-NAC model, the long-run effect of monetary policy depends on the way people form beliefs. Roger Farmer and Konstantin Platanov study a case they call 'persistent adaptive beliefs' in which people believe, correctly, that shocks to asset values are permanent. The important innovation in this work is a model of the labor market in which there can be a continuum of long- run steady state equilibria.
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When the compressive force is removed the spring returns to its original state. The minimal number of static equilibria of homogeneous, convex bodies (when resting under gravity on a horizontal surface) is of special interest. In the planar case, the minimal number is 4, while in three dimensions one can build an object with just one stable and one unstable balance point. Such an object is called a gömböc.
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Lemberg taught Ostwald many of the basics of the analysis of inorganic compounds and measurements of equilibria and chemical reaction rates. Lemberg also taught Ostwald the chemical basis of many geologic phenomena. These endeavors formed part of the subjects of Ostwald's later research efforts. Beginning during this time period, Ostwald also taught at Co-Arc from 1875 to 1881 and subsequently at Riga Polytechnicum from 1881 to 1887.
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Aside from the soluble chloride salts of divalent cations removed from the softened water, softener regeneration wastewater contains the unused 50 – 70% of the sodium chloride regeneration flushing brine required to reverse ion-exchange resin equilibria. Deionizing resin regeneration with sulfuric acid and sodium hydroxide is approximately 20–40% efficient. Neutralized deionizer regeneration wastewater contains all of the removed ions plus 2.5–5 times their equivalent concentration as sodium sulfate.Kemmer, p.
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Charge equilibria and pK values of 5-carboxypyranomalvidin-3-glucoside (vitisin A) by electrophoresis and absorption spectroscopy. Robert E. Asenstorfer and Graham P. Jones, Tetrahedron, Volume 63, Issue 22, 28 May 2007, Pages 4788-4792, Effect of acetaldehyde and several acids on the formation of vitisin A in model wine anthocyanin and colour evolution. Romero C. and Bakker J., International journal of food science & technology, 2000, vol. 35, no.
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However, because the equations are non-linear there is no guarantee of a unique solution. Furthermore, even though reasonable assumptions can guarantee that the individual excess-demand functions have a unique root, these assumptions do not guarantee that the aggregate demand does as well. There are several things to be noted. First, even though there may be multiple equilibria, every equilibrium is still guaranteed, under standard assumptions, to be Pareto efficient.
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A body can also be in a stationary state with non-zero rates of flow and chemical reaction; sometimes the word "equilibrium" is used in reference to such states, though by definition they are not thermodynamic equilibria. Sometimes, it is proposed to consider Le Chatelier's principle for such states. For this exercise, rates of flow and of chemical reaction must be considered. Such rates are not supplied by equilibrium thermodynamics.
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These JPE-papers stimulated a paper by Lloyd Shapley and Martin Shubik, which considered convexified consumer-preferences and introduced the concept of an "approximate equilibrium".: The JPE-papers and the Shapley–Shubik paper influenced another notion of "quasi-equilibria", due to Robert Aumann.: builds on two papers: Taking the convex hull of non-convex preferences had been discussed earlier by and by , according to . Non-convex sets have been incorporated in the theories of general economic equilibria,.Pages 392–399 and page 188: Pages 52–55 with applications on pages 145–146, 152–153, and 274–275: Theorem C(6) on page 37 and applications on pages 115-116, 122, and 168: These results are described in graduate-level textbooks in microeconomics, Page 628: general equilibrium theory,Page 169 in the first edition: In Ellickson, page xviii, and especially Chapter 7 "Walras meets Nash" (especially section 7.4 "Nonconvexity" pages 306–310 and 312, and also 328–329) and Chapter 8 "What is Competition?" (pages 347 and 352): game theory,Theorem 1.6.5 on pages 24–25: mathematical economics,Pages 127 and 33–34: and applied mathematics (for economists).Pages 93–94 (especially example 1.92), 143, 318–319, 375–377, and 416: Page 309: Pages 47–48: The Shapley–Folkman lemma establishes that non-convexities are compatible with approximate equilibria in markets with many consumers; these results also apply to production economies with many small firms.
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Micromagnetics is a field of physics dealing with the prediction of magnetic behaviors at sub-micrometer length scales. The length scales considered are large enough for the atomic structure of the material to be ignored (the continuum approximation), yet small enough to resolve magnetic structures such as domain walls or vortices. Micromagnetics can deal with static equilibria, by minimizing the magnetic energy, and with dynamic behavior, by solving the time-dependent dynamical equation.
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A well-known example of the minority game is the El Farol Bar problem proposed by W. Brian Arthur. A hybrid form of coordination and anti-coordination is the discoordination game, where one player's incentive is to coordinate while the other player tries to avoid this. Discoordination games have no pure Nash equilibria. In Figure 1, choosing payoffs so that A > B, C < D, while a < b, c > d, creates a discoordination game.
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In addition to the empirical concern, there has been theoretical concern. In a series of papers, Carl Bergstrom and Michael Lachmann suggest that in many biologically possible cases we should not expect to find signaling despite the fact that it is an evolutionarily stable strategy. They point out that whenever a signaling strategy is evolutionarily stable, non-signaling equilibria are as well. As a result, evolutionary stability alone does not require the evolution of signaling.
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The Van Slyke apparatus became a standard equipment in clinical laboratories around the world and the results of Van Slyke's research are still used today to determine abnormalities in the acid- base homeostasis. Later on, Van Slyke further improved his apparatus, increasing its accuracy and sensitivity. Using the new method, he was able to further investigate the role of gas and electrolyte equilibria in the blood and how they change in response to respiration.
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In addition, the concepts of correlated equilibrium, trembling hand perfection, and common knowledge were introduced and analyzed. In 2005, game theorists Thomas Schelling and Robert Aumann followed Nash, Selten, and Harsanyi as Nobel Laureates. Schelling worked on dynamic models, early examples of evolutionary game theory. Aumann contributed more to the equilibrium school, introducing equilibrium coarsening and correlated equilibria, and developing an extensive formal analysis of the assumption of common knowledge and of its consequences.
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The higher the stock of bond, investors believe the chance of default is higher. This is reasonable because more government bond put more financial restriction on the government's budget. The sunspot variable is exogenous and characterizes the uncertain properties in investors' beliefs. The paper shows that when the stock of government bond lies within certain interval, there exist multiple equilibria in which a crisis can occur stochastically, depending on the realization of the sunspot variable.
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Therefore, they proposed that a solution concept should select closed connected subsets of the set of Nash equilibria.The requirement that the set is connected excludes the trivial refinement that selects all equilibria. If only a single (possibly unconnected) subset is selected then only the trivial refinement satisfies the conditions invoked by H. Norde, J. Potters, H. Reijnierse, and D. Vermeulen (1996): ``Equilibrium Selection and Consistency, Games and Economic Behavior, 12: 219-225.
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The notion of ε-equilibria is important in the theory of stochastic games of potentially infinite duration. There are simple examples of stochastic games with no Nash equilibrium but with an ε-equilibrium for any ε strictly bigger than 0. Perhaps the simplest such example is the following variant of Matching Pennies, suggested by Everett. Player 1 hides a penny and Player 2 must guess if it is heads up or tails up.
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Octave Leopold Boudouard became a professor at the Conservatoire National des Arts et Métiers in Paris. He worked in various fields of applied chemistry, such as the chemistry of fuels and clays. His most important work was his research into chemical equilibria when reducing iron oxides in a blast furnace. In 1901 he proposed the first theory of the hydrogenation of carbon monoxide, where he considered that metal oxide was reacting with carbon.
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Frenken, K., Van Oort, F.G., Verburg, T., Boschma, R.A. (2004). Variety and Regional Economic Growth in the Netherlands – Final Report (The Hague: Ministry of Economic Affairs), 58 p. (pdf) J.S. Metcalfe noted in 1995 that "much of the traditional economic theory of technology policy is concerned with so-called 'market failures' which prevent the attainment of Pareto equilibria by violating one or other of die conditions for perfect competition".Metcalfe, J.S., 1995.
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Connie Gersick's research on the evolution of organizational systems (1988, 1991) revealed patterns of change mirroring those in biological species. Gersick examined models of change in six domains - developmental patterns of adults, groups and organizations, the history of science, physical science, and biological evolution - and found evidence for punctuated equilibria (as opposed to steady, incremental change) across those disparate systems.Gersick, Connie (1991). "Revolutionary Change Theories: A Multilevel Exploration of the Punctuated Equilibrium Paradigm".
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The UNIQUAC model can be considered a second generation activity coefficient because its expression for the excess Gibbs energy consists of an entropy term in addition to an enthalpy term. Earlier activity coefficient models such as the Wilson equation and the non-random two-liquid model (NRTL model) only consist of enthalpy terms. Today the UNIQUAC model is frequently applied in the description of phase equilibria (i.e. liquid–solid, liquid–liquid or liquid–vapor equilibrium).
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In mathematics, a heteroclinic cycle is an invariant set in the phase space of a dynamical system. It is a topological circle of equilibrium points and connecting heteroclinic connectionss. If a heteroclinic cycle is asymptotically stable, approaching trajectories spend longer and longer periods of time in a neighbourhood of successive equilibria. In generic dynamical systems heteroclinic connections are of high co-dimension, that is, they will not persist if parameters are varied.
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In the early seventies, motivated by the potential role of price rigidities for enhancing risk-sharing efficiency, Jacques Drèze undertook to define equilibria with price rigidities and quantity constraints and to study their properties in a general equilibrium context. His 1975 paper (36, circulated in 1971) introduces the so-called "Drèze equilibrium" at which supply (resp. demand) is constrained only when prices are downward (resp. upward) rigid, whereas a preselected commodity (e.g.
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In the early seventies, motivated by the potential role of price rigidities for enhancing risk-sharing efficiency, Jacques Drèze undertook to define equilibria with price rigidities and quantity constraints and to study their properties in a general equilibrium context. His 1975 paper (36, circulated in 1971) introduces the so-called "Drèze equilibrium" at which supply (resp. demand) is constrained only when prices are downward (resp. upward) rigid, whereas a preselected commodity (e.g.
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The two pure strategy Nash equilibria are unfair; one player consistently does better than the other. The mixed strategy Nash equilibrium (when it exists) is inefficient. The players will miscoordinate with probability 13/25, leaving each player with an expected return of 6/5 (less than the return one would receive from constantly going to one's less favored event). One possible resolution of the difficulty involves the use of a correlated equilibrium.
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That is, if any player \,i chooses a higher \,z_i, all other players \,j have an incentive to raise their choices \,z_j too. Following the terminology of Bulow, Geanakoplos, and Klemperer (1985), economists call this situation strategic complementarity, because players' strategies are complements to each other. This is the basic property underlying examples of multiple equilibria in coordination games. The opposite case of submodularity of \,f corresponds to the situation of strategic substitutability.
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We need to broaden the concept of a tangent to include any line which touches the curve: a tangent in the etymological sense rather than that of the differential calculus. In the example of Fig. 12 there is an arc of legal price lines through a point of contact, each touching indifference curves without cutting them inside the box, and accordingly there is a range of possible equilibria for a given endowment.
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The equilibria of Fig. 12 are not points at which curves are true tangents to each other. They do however have a property which generalises the definition in terms of tangents, which is that the two curves can be locally separated by a straight line. Arror and Debreu defined equilibrium in the same way as each other in their (independent) papers of 1951 without providing any source or rationale for their definition.
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The profile of equilibrium unfolding may enable one to detect and identify intermediates of unfolding. General equations have been developed by Hugues Bedouelle to obtain the thermodynamic parameters that characterize the unfolding equilibria for homomeric or heteromeric proteins, up to trimers and potentially tetramers, from such profiles. Fluorescence spectroscopy can be combined with fast-mixing devices such as stopped flow, to measure protein folding kinetics, generate a chevron plot and derive a Phi value analysis.
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Manganese(II) diselenide is the inorganic compound with the formula MnSe2. This rarely encountered solid is structurally similar to that of iron pyrite (FeS2). Analogous to the description of iron pyrite, manganese diselenide is sometimes viewed as being composed of Mn2+ and Se22− ions, although being a semiconductor, MnSe2 is not appropriately described in formal oxidation states."The Mn-Se (Manganese-selenium) System" Journal of Phase Equilibria , Volume 19, Number 6 , 12/1998 , pp.
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It gave rise to social choice theory with the introduction of his "Possibility Theorem". This sparked widespread discussion over how to interpret the different conditions of the theorem and what implications it had for democracy and voting. Most controversial of his four (1963) or five (1950/1951) conditions is the independence of irrelevant alternatives. In the 1950s Kenneth Arrow and Gérard Debreu (1921–2004) developed the Arrow–Debreu model of general equilibria.
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Friedrich Wilhelm Ostwald (4 April 1932) was a Baltic German chemist and philosopher. He received the Nobel Prize in Chemistry in 1909 for his scientific contributions to the fields of catalysis, chemical equilibria and reaction velocities. Ostwald, Jacobus Henricus van 't Hoff, Walther Nernst, and Svante Arrhenius are credited with being the founders of the field of physical chemistry. Following his 1906 retirement from academic life, Ostwald became much involved in philosophy, art, and politics.
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In fact, strong Nash equilibrium has to be Pareto-efficient. As a result of these requirements, Strong Nash rarely exists in games interesting enough to deserve study. Nevertheless, it is possible for there to be multiple strong Nash equilibria. For instance, in Approval voting, there is always a strong Nash equilibrium for any Condorcet winner that exists, but this is only unique (apart from inconsequential changes) when there is a majority Condorcet winner.
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Hydrogenotrophic methanogens utilize CO2 and H2 to produce methane by the following reaction: : CO2 \+ 4H2 → CH4 \+ 2H2O Acetoclastic methanogens metabolize acetate acid and produce methane: : CH3COOH → CH4 \+ CO2 In laboratories, clumped isotope compositions of methane generated by hydrogenotrophic methanogens, acetoclastic methanogens (biodegradation of acetate), and methylotrophic methanogens are universally out of equilibria. It has been proposed that the reversibility of methanogenic enzyme is key to the kinetic isotope effect expressed in biogenic methane.
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A number of important problem classes can be solved. Specific examples are variational inequalities, Nash equilibria, disjunctive programs and stochastic programs. EMP is independent of the modeling language used but currently it is implemented only in GAMS. The new types of problems modeled with EMP are reformulated with the GAMS solver JAMS to well established types of problems and the reformulated models are passed to a suitable GAMS solver to be solved.
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Athey's early contributions included a new way to model uncertainty (the subject of her doctoral dissertation) and understand investor behavior given uncertainty, along with insights into the behavior of auctions. Athey's research on decision-making under uncertainty focused on conditions under which optimal decision policies would be monotone in a given parameter. She applied her results to establish conditions under which Nash equilibria would exist in auctions and other Bayesian games. Athey's work changed the way auctions are held.
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Stemming from the article by Milgrom and Shannon as well as the results obtained by VeinottVeinott (1992): Lattice programming: qualitative optimization and equilibria. MS Stanford. and TopkisSee: Topkis, D. M. (1979): “Equilibrium Points in Nonzero-Sum n-Person Submodular Games,” SIAM Journal of Control and Optimization, 17, 773–787; as well as Topkis, D. M. (1998): Supermodularity and Complementarity, Frontiers of economic research, Princeton University Press, . an important strand of operational research was developed called monotone comparative statics.
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Essentially, life as a continuum of contingent experiences reflects the doctrine of Heracletan flux that greatly influenced the course of Western philosophy. This outlook begs on the part of the subject a reorientation of all outlying perceptions and ultimately renders all teleological equilibria as purely theoretical conceptions. In the midst of flux, the subject is made a victim of his or her circumstance. The Polifemo reflects a change in the aesthetic and philosophical perceptions of 17th- century Europe.
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Smaller objects (green) at the Lagrange points are in equilibrium. At any other point, the gravitational forces are non equilibria. Lagrange points in the Sun–Earth system (not to scale) – a small object at any one of the five points will hold its relative position. An example of a spacecraft at Sun–Earth L2 In celestial mechanics, the Lagrange points ( also Lagrangian points, L-points, or libration points) are orbital points near two large co-orbiting bodies.
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A four-stage centipede game The primary use of game theory is to describe and model how human populations behave. Some scholars believe that by finding the equilibria of games they can predict how actual human populations will behave when confronted with situations analogous to the game being studied. This particular view of game theory has been criticized. It is argued that the assumptions made by game theorists are often violated when applied to real-world situations.
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Moreover, the set {Alice} is super-self-sufficient, because Alice holds guavas which are worthless to her. Indeed, a competitive equilibrium does not exist: regardless of the price, Alice would like to give all her guavas for apples, but George has no apples so her demand will remain unfulfilled. C. Many equilibria: Suppose there are two goods and two agents, both agents assign the same value to both goods (e.g. for both of them, w_{apples}=w_{guavas}=1).
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Marge had seven sisters (including one who died in early childhood), and brother Grant R. Williams who died as a Navy test pilot. Asprey was discharged from the Army in February 1946. He decided to enter the University of California, Berkeley, and get his Ph.D. in chemistry under the supervision of Burris B. Cunningham, whom he had worked for at the Metallurgical Laboratory. He wrote his thesis on "Equilibria in the oxide systems of praseodymium and americium".
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Cheltenham, UK: Edward Elgar Publishing. , pages 140-1. Russell Cooper and Andrew John's 1988 paper Coordinating Coordination Failures in Keynesian Models expressed a general form of coordination as models with multiple equilibria where agents could coordinate to improve (or at least not harm) each of their respective situations.Howitt (2002), page142 Cooper and John based their work on earlier models including Peter Diamond's 1982 coconut model, which demonstrated a case of coordination failure involving search and matching theory.
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In game theory, normal form is a description of a game. Unlike extensive form, normal-form representations are not graphical per se, but rather represent the game by way of a matrix. While this approach can be of greater use in identifying strictly dominated strategies and Nash equilibria, some information is lost as compared to extensive-form representations. The normal- form representation of a game includes all perceptible and conceivable strategies, and their corresponding payoffs, for each player.
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Bayesian Nash equilibrium can result in implausible equilibria in dynamic games, where players move sequentially rather than simultaneously. As in games of complete information, these can arise via non- credible strategies off the equilibrium path. In games of incomplete information there is also the additional possibility of non-credible beliefs. To deal with these issues, Perfect Bayesian equilibrium, in the spirit of subgame perfect equilibrium requires that, starting from any information set, subsequent play be optimal.
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In this way, microscopic reversibility was used to prove macroscopic irreversibility and convergence of ensembles of molecules to their thermodynamic equilibria. Another macroscopic consequence of microscopic reversibility is the symmetry of kinetic coefficients, the so-called reciprocal relations. The reciprocal relations were discovered in the 19th century by Thomson and Helmholtz for some phenomena but the general theory was proposed by Lars Onsager in 1931. He found also the connection between the reciprocal relations and detailed balance.
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With the CALPHAD method one collects all experimental information on phase equilibria in a system and all thermodynamic information obtained from thermochemical and thermophysical studies. The thermodynamic properties of each phase are then described with a mathematical model containing adjustable parameters. The parameters are evaluated by optimizing the fit of the model to all the information, also involving coexisting phases. It is then possible to recalculate the phase diagram as well as the thermodynamic properties of all the phases.
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Phyletic gradualism, top, would consist of steady evolutionary change in small steps, in contrast to punctuated equilibrium Apparently sudden changes can be explained either by macromutation or by relatively rapid episodes of gradual evolution, since 10,000 years barely registers in the fossil record. Phyletic gradualism is a model of evolution which theorizes that most speciation is slow, uniform and gradual.Eldredge, N. and S. J. Gould (1972). "Punctuated equilibria: an alternative to phyletic gradualism" In T.J.M. Schopf, ed.
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The Calvin cycle uses the energy from short-lived electronically excited carriers to convert carbon dioxide and water into organic compounds that can be used by the organism (and by animals that feed on it). This set of reactions is also called carbon fixation. The key enzyme of the cycle is called RuBisCO. In the following biochemical equations, the chemical species (phosphates and carboxylic acids) exist in equilibria among their various ionized states as governed by the pH.
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The reaction mechanism displayed below demonstrates step by step how hexamine donates a methine group to an aromatic substrate via a series of equilibria reactions, with iminium ion intermediates. Initially, addition to the aromatic ring results in an intermediate at the oxidation state of a benzylamine. An intramolecular redox reaction then ensues, raising the benzylic carbon to the oxidation state of an aldehyde. The oxygen atom is provided by water on acid hydrolysis in the final step.
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A model organized around the tâtonnement process has been said to be a model of a centrally planned economy, not a decentralized market economy. Some research has tried to develop general equilibrium models with other processes. In particular, some economists have developed models in which agents can trade at out-of-equilibrium prices and such trades can affect the equilibria to which the economy tends. Particularly noteworthy are the Hahn process, the Edgeworth process and the Fisher process.
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One distinction separated the similarity and difference of any pair in the minimum triple. However, his formal methods denied the competence of mathematics or digital serial and parallel processes to produce applicable descriptions because of their innate pathologies in locating the infinitesimals of dynamic equilibria (Stafford Beer's "Point of Calm"). He dismissed the digital computer as a kind of kinematic "magic lantern". He saw mechanical models as the future for the concurrent kinetic computers required to describe natural processes.
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With recent advances in rotational viscometry techniques, viscosities of iron oxide slags are also widely undertaken. Coupled with phase equilibria studies, these analysis provide a better understanding of physico-chemical behaviour of slags at high temperatures. In the early stages of smelting, separation between melting metal and slag is not complete. Hence, the main, minor and trace elements of metal in the slag can be indicators of the type of ore used in the smelting process.
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Thiocyanogen, (SCN)2, is a pseudohalogen derived from the pseudohalide thiocyanate, [SCN]−. This hexatomic compound exhibits C2 point group symmetry and has the connectivity NCS-SCN. The oxidation ability is greater than bromine. It reacts with water: 3(SCN)2 \+ 4H2O → H2SO4 \+ HCN + 5SCN− \+ 5H+ Thiocyanogen was originally prepared by the reaction of iodine with a suspension of silver thiocyanate in diethyl ether, but this reaction suffers from competing equilibria attributed to the weak oxidizing power of iodine.
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J. Willard Gibbs formulated a concept of thermodynamic equilibrium of a system in terms of energy and entropy. He also did extensive work on chemical equilibrium, and equilibria between phases. American mathematical physicist J. Willard Gibbs's work on the applications of thermodynamics was instrumental in transforming physical chemistry into a rigorous deductive science. During the years from 1876 to 1878, Gibbs worked on the principles of thermodynamics, applying them to the complex processes involved in chemical reactions.
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Solubility equilibrium is a type of dynamic equilibrium that exists when a chemical compound in the solid state is in chemical equilibrium with a solution of that compound. The solid may dissolve unchanged, with dissociation or with chemical reaction with another constituent of the solution, such as acid or alkali. Each solubility equilibrium is characterized by a temperature- dependent solubility product which functions like an equilibrium constant. Solubility equilibria are important in pharmaceutical, environmental and many other scenarios.
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The UNIFAC Consortium has been founded at the Carl von Ossietzky University of Oldenburg at the chair of industrial chemistry of Prof. Gmehling to invite private companies to support the further development of the group contribution methods UNIFAC and its successor modified UNIFAC (Dortmund). Both models are used for the prediction of thermodynamic properties, especially the estimation of phase equilibria. The UNIFAC consortium is a successful example of private sponsorship of a public university in Germany.
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The game is analogous to the war of attrition and penny auction and has a symmetric mixed strategy equilibrium (there are also asymmetric pure equilibria). Suppose we start with two players; player 1 moves in odd periods, while player 2 moves in even periods. When a player is behind, they are indifferent between raising and dropping out. If the opponent drops out with probability p, raising gives the player an expected payoff of p\times1+(1-p)\times0-0.05.
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The NRTL parameter set to use depends on the kind of phase equilibrium (i.e. solid–liquid (SL), liquid–liquid (LL), vapor–liquid (VL)). In the case of the description of a vapor–liquid equilibria it is necessary to know which saturated vapor pressure of the pure components was used and whether the gas phase was treated as an ideal or a real gas. Accurate saturated vapor pressure values are important in the determination or the description of an azeotrope.
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During the 1990s he worked mostly on approximation algorithms, championing the primal-dual schema, which he applied to problems arising in network design, facility location. See and web caching, and clustering. In July 2001 he published what is widely regarded as the definitive book on approximation algorithms (Springer-Verlag, Berlin). Since 2002, he has been at the forefront of the effort to understand the computability of market equilibria, with an extensive body of work on the topic.
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In 1966, he became a professor at Yale University. He was Professor of Astrophysical Sciences in 1967 until he retired in 2004. In 1993, he received the James Clerk Maxwell Prize in Plasma Physics for "his pioneering contributions to basic plasma theory, to the physics of magnetically confined plasmas, and to plasma astrophysics. His important work en-compasses plasma equilibria and stability, adiabatic invariance, ballooning modes, runaway electrons, colliding beams, spin-polarized plasmas, and cosmic-ray instabilities".
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Turner continued to work in the field, refining the metamorphic facies classifications through the end of his career in the early 1970s. Triangular diagrams showing the aluminium (A), calcium (C) and iron (F) content of the main phases (dark dots) in metamorphic rocks in various facies. Thin grey lines are stable phase equilibria. Triangular diagrams showing the aluminium (A), iron (F) and magnesium (M) content of the main phases (dark dots and, when the composition can vary, stripes).
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Many industries have been cited as oligopolistic, including civil aviation,Adriana Gama, Review of Regulating the Polluters: Markets and Strategies for Protecting the Global Environment by Alexander Ovodenko, Global Environmental Politics, MIT Press, Vol. 19, No. 3, August 2019, pp. 143-145. agricultural pesticides, electricity,Seyedamirabbas Mousavian, Antonio J. Conejo & Ramteen Sioshansi, Equilibria in investment and spot electricity markets: A conjectural-variations approach, European Journal of Operational Research, Vol. 281, Issue 1 (Feb. 2020), pp. 129-140.
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According to Gibbs' rules of phase equilibria, these unique crystalline phases are dependent on intensive variables such as pressure and temperature. Polymorphism is related to allotropy, which refers to elemental solids. The complete morphology of a material is described by polymorphism and other variables such as crystal habit, amorphous fraction or crystallographic defects. Polymorphs have different stabilities and may spontaneously and irreversibly transform from a metastable form (or thermodynamically unstable form) to the stable form at a particular temperature.
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An amphoteric substance is one that can act as an acid or as a base, depending on pH. Water (below) is amphoteric. Another example of an amphoteric molecule is the bicarbonate ion that is the conjugate base of the carbonic acid molecule H2CO3 in the equilibrium :H2CO3 \+ H2O + H3O+ but also the conjugate acid of the carbonate ion in (the reverse of) the equilibrium : + OH− \+ H2O. Carbonic acid equilibria are important for acid–base homeostasis in the human body.
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The structure of a foldamer can often be predicted from its primary sequence. This process involves dynamic simulations of the folding equilibria at the atomic level under various conditions. This type of analysis may be applied to small proteins as well, however computational technology is unable to simulate all but the shortest of sequences. The folding pathway of a foldamer can be determined by measuring the variation from the experimentally determined favored structure under different thermodynamic and kinetic conditions.
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A relatively weaker yet refined Nash stability concept is called coalition-proof Nash equilibrium (CPNE) in which the equilibria are immune to multilateral deviations that are self-enforcing. Every correlated strategy supported by iterated strict dominance and on the Pareto frontier is a CPNE. Further, it is possible for a game to have a Nash equilibrium that is resilient against coalitions less than a specified size k. CPNE is related to the theory of the core.
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It can be used to prove the Hartman-Grobman theorem, which describes the qualitative behaviour of certain differential equations near certain equilibria. Similarly, Brouwer's theorem is used for the proof of the Central Limit Theorem. The theorem can also be found in existence proofs for the solutions of certain partial differential equations.These examples are taken from: F. Boyer Théorèmes de point fixe et applications CMI Université Paul Cézanne (2008–2009) Archived copy at WebCite (August 1, 2010).
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Since many linear and nonlinear systems that oscillate are modeled as harmonic oscillators near their equilibria, this section begins with a derivation of the resonant frequency for a driven, damped harmonic oscillator. The section then uses an RLC circuit to illustrate connections between resonance and a system's transfer function, frequency response, poles, and zeroes. Building off the RLC circuit example, the section then generalizes these relationships for higher- order linear systems with multiple inputs and outputs.
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The potential for tactical voting in a single non-transferable vote system is large. Receiving only one vote, the rational voter must only vote for a candidate that has a chance of winning, but will not win by too great a margin, thus taking votes away from party colleagues. This also creates opportunities for tactical nominations, with parties nominating candidates similar to their opponents' candidates in order to split the vote. SNTV has been measured through the lens of such concepts as decision-theoretic analysis. Professor Gary W. Cox, an expert on SNTV, has studied this system’s use in Japan.Cox G.W. “Strategic Voting Equilibria Under the Single Nontransferable Vote.” The American Political Science Review 88.3 (Sep., 1994) 608 Print Cox has an explanation of real-world data finding the, “two systems [plurality and semi- proportional] are alike in their strategic voting equilibria.”Cox 608 His research found that voters use the information offered in campaigns (polls, reporting, fundraising totals, endorsements, etc.), to rationally decide who the most viable candidates are and then vote for them.
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In the early 1970s, Weber proposed an alternative to the traditional "plurality rule" for elections involving more than two candidates. This alternative, which he named "approval voting", a multi-candidate binary rating system of social choice, has generated a substantial body of research, has been adopted by a number of professional organizations, and has been used in several public elections. His later work in this area includes "A Theory of Voting Equilibria", co-authored with Roger Myerson. For a summary see "Approval Voting".
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There are several advantages to using smoothed best response, both theoretical and empirical. First, it is consistent with psychological experiments; when individuals are roughly indifferent between two actions they appear to choose more or less at random. Second, the play of individuals is uniquely determined in all cases, since it is a correspondence that is also a function. Finally, using smoothed best response with some learning rules (as in Fictitious play) can result in players learning to play mixed strategy Nash equilibria .
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Last closed magnetic flux surfaces as reconstructed by the V3FIT code without (left) and with (right) plasma current. The coloration depicts the strength of the magnetic field with red being the strongest field and blue being the weakest. Sample field lines are shown in white. V3FIT is a code to reconstruct the equilibrium between the plasma and confining magnetic field in cases where the magnetic field is toroidal in nature, but not axisymmetric as is the case with tokamak equilibria.
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This may result in a no equilibrium being found, and stems from dropping the assumption for the existence of a Nash equilibrium that the game be finite or that the game have complete information. Another possibility is the existence of a rule which allows a dictator to force an equilibrium. The rules which make up the norms of the game are one way of resolving the problem of choosing between multiple equilibria, such as those arising in the so-called folk theorem.
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When consumer preferences have concavities, then the linear budgets need not support equilibria: Consumers can jump between allocations. If a preference set is non‑convex, then some prices produce a budget supporting two different optimal consumption decisions. For example, we can imagine that, for zoos, a lion costs as much as an eagle, and further that a zoo's budget suffices for one eagle or one lion. We can suppose also that a zoo-keeper views either animal as equally valuable.
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Unlike those in economics, the payoffs for games in biology are often interpreted as corresponding to fitness. In addition, the focus has been less on equilibria that correspond to a notion of rationality and more on ones that would be maintained by evolutionary forces. The best-known equilibrium in biology is known as the evolutionarily stable strategy (ESS), first introduced in . Although its initial motivation did not involve any of the mental requirements of the Nash equilibrium, every ESS is a Nash equilibrium.
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One of the earlier published theoretical research addressing properties of auctions among asymmetric bidders is Keith Waehrer's 1999 article.K. Waehrer (1999) "Asymmetric Auctions With Application to Joint Bidding and Mergers," International Journal of Industrial Organization 17: 437–452 Later published research include Susan Athey's 2001 Econometrica article,Athey, S. (2001) "Single Crossing Properties and the Existence of Pure Strategy Equilibria in Games of Incomplete Information," Econometrica Vol. 69 No. 4, pp. 861–890. as well as Reny and Zamir (2004).
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The UNIFAC model was first published in 1975 by Fredenslund, Jones and Prausnitz, a group of chemical engineering researchers from the University of California. Subsequently they and other authors have published a wide range of UNIFAC papers, extending the capabilities of the model; this has been by the development of new or revision of existing UNIFAC model parameters. UNIFAC is an attempt by these researchers to provide a flexible liquid equilibria model for wider use in chemistry, the chemical and process engineering disciplines.
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In the mathematics of evolving systems, the concept of a center manifold was originally developed to determine stability of degenerate equilibria. Subsequently, the concept of center manifolds was realised to be fundamental to mathematical modelling. Center manifolds play an important role in bifurcation theory because interesting behavior takes place on the center manifold and in multiscale mathematics because the long time dynamics of the micro-scale often are attracted to a relatively simple center manifold involving the coarse scale variables.
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Kalai's work on large games showed that the equilibria of Bayesian games with many players are structurally robust, thus large games escape major pitfalls in game-theoretic modeling. Kalai is also known for seminal collaborative research on flow games and totally balanced games; strategic complexity and its implications in economics and political systems; arbitration, strategic delegation and commitments; extensions of Arrow’s Impossibility Theorem in social choice; competitive service speed in queues; and on rational strategic polarization in group decision making.
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Work by Michael Mandler (1999) has challenged this claim. The Arrow–Debreu–McKenzie model is neutral between models of production functions as continuously differentiable and as formed from (linear combinations of) fixed coefficient processes. Mandler accepts that, under either model of production, the initial endowments will not be consistent with a continuum of equilibria, except for a set of Lebesgue measure zero. However, endowments change with time in the model and this evolution of endowments is determined by the decisions of agents (e.g.
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In 1996, he received the James Clerk Maxwell Prize for Plasma Physics for "seminal contributions to plasma theory, including extension of Landau damping to the nonlinear regime and demonstration of the importance of particle trapping; discovery of the plasma-wave echo; and pioneering studies of the confinement, transport, and thermal equilibria of non-neutral plasmas, liquids and crystals. His theoretical work and active guidance of experiments with trapped, non-neutral plasmas provide much of the foundation for this branch of plasma physics".
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This dependence on pore geometry and curvature can result in hysteresis and vastly different liquid/vapor equilibria over very small ranges in pressure. It is also worthy to mention that different pore geometries result in different types of curvature. In scientific studies of capillary condensation, the hemispherical meniscus situation (that resulting from a perfectly cylindrical pore) is most often investigated due to its simplicity. Cylindrical menisci are also useful systems because they typically result from scratches, cuts, and slit-type capillaries in surfaces.
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Since producers search for food and scroungers wait for opportunities to join, prey crypsis imposes a producer specific cost that shifts the producer scrounger equilibria towards more scrounging. Prey crypsis resulted in increased latency to eat the seed and increased number of detection errors. Moreover, the presence of a competitor negatively affected foraging efficiency under cyptic backgrounds. The foraging efficiency of individuals that had previously foraged with a competitor on cryptic seeds remained low even after the competitor had been removed.
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They are an intermediate step in the oxidation of ammonia to nitrite, which occurs in the nitrogen cycle. Hyponitrite can act as a bridging or chelating bidentate ligand.Greenwood and Earnshaw, pp. 459–72 Nitrous acid (HNO2) is not known as a pure compound, but is a common component in gaseous equilibria and is an important aqueous reagent: its aqueous solutions may be made from acidifying cool aqueous nitrite (, bent) solutions, although already at room temperature disproportionation to nitrate and nitric oxide is significant.
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Global coordination games belong to a subfield of game theory which gained momentum with the article by Morris and Shin (1998). Stephen Morris and Hyun Song Shin considered a stylized currency crises model, in which traders observe the relevant fundamentals with small noise, and show that this leads to the selection of a unique equilibrium. This result is in stark contrast with models of complete information, which feature multiple equilibria. Morris has also made important contributions to the theory of mechanism design.
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In the mathematical area of bifurcation theory a saddle-node bifurcation, tangential bifurcation or fold bifurcation is a local bifurcation in which two fixed points (or equilibria) of a dynamical system collide and annihilate each other. The term 'saddle-node bifurcation' is most often used in reference to continuous dynamical systems. In discrete dynamical systems, the same bifurcation is often instead called a fold bifurcation. Another name is blue sky bifurcation in reference to the sudden creation of two fixed points.
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Variation of log Kc of acetic acid with ionic strength It is very rare for activity coefficient values to have been determined experimentally for a system at equilibrium. There are three options for dealing with the situation where activity coefficient values are not known from experimental measurements. #Use calculated activity coefficients, together with concentrations of reactants. For equilibria in solution estimates of the activity coefficients of charged species can be obtained using Debye–Hückel theory, an extended version, or SIT theory.
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Generally speaking, an equilibrium is defined to be the price-quantity pair where the quantity demanded is equal to the quantity supplied. It is represented by the intersection of the demand and supply curves. The analysis of various equilibria is a fundamental aspect of microeconomics: Market equilibrium: A situation in a market when the price is such that the quantity demanded by consumers is correctly balanced by the quantity that firms wish to supply. In this situation, the market clears.
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If we have a function which describes the system's potential energy, we can determine the system's equilibria using calculus. A system is in mechanical equilibrium at the critical points of the function describing the system's potential energy. We can locate these points using the fact that the derivative of the function is zero at these points. To determine whether or not the system is stable or unstable, we apply the second derivative test: Diagram of a ball placed in an unstable equilibrium.
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If the players do not know which player they are then no uncorrelated asymmetry exists. The information asymmetry is that one player believes he is player 1 and the other believes he is player 2. Therefore, "informational asymmetry" does not refer to knowledge in the sense of an information set in an extensive form game. The concept of uncorrelated asymmetries is important in determining which Nash equilibria are evolutionarily stable strategies in discoordination games such as the game of chicken.
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In sharp contrast to hydrocarbon-derived ketones, whose enol tautomers are generally present in only trace quantities at equilibrium, fluorinated ketones are sometimes far less stable than their enols. Keto-enol equilibria for cyclopentanone (11) and heptafluorocyclopentanone (12) are a case in point. In sharp contrast to hydrocarbon-derived ketones, whose enol tautomers are generally present in only trace quantities at equilibrium, fluorinated ketones are sometimes far less stable than their enols. Highly strained and highly reactive alkenes bicyclo[2.2.
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Following earlier ideas by Nelson (1970, 1974), Milgrom and Roberts (1986) show that even "uninformative" advertising, that is, advertising expenditures that provide no direct information about a product's characteristics, may be informative in equilibrium to the extent that they work as a signal of the advertiser's quality level. Methodologically, Milgrom and Roberts (1986) also make an important contribution: the study of signaling equilibria when the informed party has more than one available signal (price and advertising, in the present case).
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Milgrom's 1985 paper with Robert J. Weber on distributional strategies showed the general existence of equilibria for a Bayesian game with finitely many players, if the players' sets of types and actions are compact metric spaces, the players' payoffs are continuous functions of the types and actions, and the joint distribution of the players' types is absolutely continuous with respect to the product of their marginal distributions. These basic assumptions are always satisfied if the sets of types and actions are finite.
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VTPR (short for Volume-Translated Peng–Robinson)Ahlers J., "Entwicklung einer universellen Gruppenbeitragszustandsgleichung", Thesis, Carl-von-Ossietzky- Universität Oldenburg, 1-144, 2003Schmid B., "Einsatz einer modernen Gruppenbeitragszustandsgleichung für die Synthese thermischer Trennprozesse", Thesis, C.v.O. Universität Oldenburg, 2011 is an estimation method for the calculation of phase equilibria of mixtures of chemical components. The original goal for the development of this method was to enable the estimation of properties of mixtures which contain supercritical components. These class of substances couldn't be predicted with established models like UNIFAC.
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Following the death of Judge Rolin- Jaequemyns in 1936, de Visscher was appointed as Belgium's ad hoc judge in the Permanent Court of International Justice. He was elected a full judge in 1937, in which position he served until the court's dissolution. He subsequently served on the International Court of Justice from 1946 until 1951. Couvreur states that the consensus is de Visscher's not being re-elected, while unexpected, was due to "the subtle interplay of political equilibria", rather than any particular failing of de Visscher himself.
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Handbook of Developmental Science, Behavior, and Genetics. Wiley-Blackwell. p. 70 Lovtrup believed that macromutations interfered with various epigenetic processes, that is, those which affect the causal processes in biological development. This is in contrast to the gradualistic theory of micromutations of Neo-Darwinism, which claims that evolutionary innovations are generally the result of accumulation of numerous very slight modifications. Lovtrup also rejected the punctuated equilibria of Stephen Gould and Niles Eldredge, claiming it was a form of gradualism and not a macromutation theory.
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It was in the course of proving of the existence of an optimal equilibrium in his 1937 model of economic growth that John von Neumann introduced functional analytic methods to include topology in economic theory, in particular, fixed-point theory through his generalization of Brouwer's fixed-point theorem.Andrew McLennan, 2008. "fixed point theorems", The New Palgrave Dictionary of Economics, 2nd Edition. Abstract. Following von Neumann's program, Kenneth Arrow and Gérard Debreu formulated abstract models of economic equilibria using convex sets and fixed–point theory.
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Game theorists usually assume players act rationally, but in practice, human behavior often deviates from this model. Game theorists respond by comparing their assumptions to those used in physics. Thus while their assumptions do not always hold, they can treat game theory as a reasonable scientific ideal akin to the models used by physicists. However, empirical work has shown that in some classic games, such as the centipede game, guess 2/3 of the average game, and the dictator game, people regularly do not play Nash equilibria.
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If a player A has a dominant strategy s_A then there exists a Nash equilibrium in which A plays s_A. In the case of two players A and B, there exists a Nash equilibrium in which A plays s_A and B plays a best response to s_A. If s_A is a strictly dominant strategy, A plays s_A in all Nash equilibria. If both A and B have strictly dominant strategies, there exists a unique Nash equilibrium in which each plays their strictly dominant strategy.
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MIRI has also published Inadequate Equilibria, Yudkowsky's 2017 ebook on the subject of societal inefficiencies. Yudkowsky has also written several works of fiction. His fanfiction novel, Harry Potter and the Methods of Rationality, uses plot elements from J.K. Rowling's Harry Potter series to illustrate topics in science."'Harry Potter' and the Key to Immortality", Daniel Snyder, The Atlantic The New Yorker described Harry Potter and the Methods of Rationality as a retelling of Rowling's original "in an attempt to explain Harry's wizardry through the scientific method".
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In fact, the only stable states in the two population model correspond to the pure strategy equilibria, where one population is composed of all Hawks and the other of all Doves. In this model one population becomes the aggressive population while the other becomes passive. This model is illustrated by the vector field pictured in Figure 7a. The one-dimensional vector field of the single population model (Figure 7b) corresponds to the bottom left to top right diagonal of the two population model. Fig.
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Kaldor recommended that von Neumann read a book by the mathematical economist Léon Walras. Von Neumann found some faults in the book and corrected them–for example, replacing equations by inequalities. He noticed that Walras's General Equilibrium Theory and Walras's Law, which led to systems of simultaneous linear equations, could produce the absurd result that profit could be maximized by producing and selling a negative quantity of a product. He replaced the equations by inequalities, introduced dynamic equilibria, among other things, and eventually produced the paper.
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Computerized databases often include subroutines for calculating reaction properties and displaying the data as charts. Thermodynamic data comes from many types of experiments, such as calorimetry, phase equilibria, spectroscopy, composition measurements of chemical equilibrium mixtures, and emf measurements of reversible reactions. A proper database takes all available information about the elements and compounds in the database, and assures that the presented results are internally consistent. Internal consistency requires that all values of the thermodynamic functions are correctly calculated by application of the appropriate thermodynamic equations.
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Thus the fossil record suggests that evolution occurs in bursts, interspersed by long periods of evolutionary stagnation in so-called punctuated equilibria. Why this is so has been an evolutionary enigma ever since Darwin first recognized the problem. Koinophilia could explain both the horizontal and vertical manifestations of speciation, and why it, as a general rule, involves the entire external appearance of the animals concerned. Since koinophilia affects the entire external appearance, the members of an interbreeding group are driven to look alike in every detail.
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In game theory, the price of stability (PoS) of a game is the ratio between the best objective function value of one of its equilibria and that of an optimal outcome. The PoS is relevant for games in which there is some objective authority that can influence the players a bit, and maybe help them converge to a good Nash equilibrium. When measuring how efficient a Nash equilibrium is in a specific game we often time also talk about the price of anarchy (PoA).
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The concept of a thermodynamic template is demonstrated in scheme 1. A thermodynamic template is a reagent that can stabilize the form of one product over others by lowering it's Gibb's free energy (ΔG°) in relation to other products. cyclophane C2 can be prepared by the irreversible highly diluted reaction of a diol with chlorobromomethane in the presence of sodium hydride. The dimer however is part of series of equilibria between polyacetal macrocycles of different size brought about by acid catalyzed (triflic acid) transacetalization.
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Then, if an equilibrium is unstable and there is a shock, the economy will wind up at a different set of allocations and prices once the convergence process terminates. However stability depends not only on the number of equilibria but also on the type of the process that guides price changes (for a specific type of price adjustment process see Walrasian auction). Consequently, some researchers have focused on plausible adjustment processes that guarantee system stability, i.e., that guarantee convergence of prices and allocations to some equilibrium.
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A classic example of a dynamic game with complete information is Stackelberg's (1934) sequential-move version of Cournot duopoly. Other examples include Leontief's (1946) monopoly-union model and Rubenstein's bargaining model. Lastly, when complete information is unavailable (incomplete information games), these solutions turn towards Bayesian Nash Equilibria since games with incomplete information become Bayesian games. In a game of complete information, the players' payoffs functions are common knowledge, whereas in a game of incomplete information at least one player is uncertain about another player's payoff function.
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Cooper and John based their work on earlier models including Peter Diamond's (1982) coconut model, which demonstrated a case of coordination failure involving search and matching theory. In Diamond's model producers are more likely to produce if they see others producing. The increase in possible trading partners increases the likelihood of a given producer finding someone to trade with. As in other cases of coordination failure, Diamond's model has multiple equilibria, and the welfare of one agent is dependent on the decisions of others.
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Crystalline materials are never perfect on a microscale. Some sites of atoms in the crystal lattice can be occupied by point defects, such as "alien" particles or vacancies. Vacancies can actually be thought of as chemical species themselves (or part of a compound species/component) that may then be treated using heterogeneous phase equilibria. The number of vacancies may also be influenced by the number of chemical impurities in the crystal lattice, if such impurities require the formation of vacancies to exist in the lattice.
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The 'second generation' of models of currency crises starts with the paper of Obstfeld (1986). In these models, doubts about whether the government is willing to maintain its exchange rate peg lead to multiple equilibria, suggesting that self-fulfilling prophecies may be possible. Specifically, investors expect a contingent commitment by the government and if things get bad enough, the peg is not maintained. For example, in the 1992 ERM crisis, the UK was experiencing an economic downturn just as Germany was booming due to the reunification.
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Many other amine complexes of the platinum group metals have been evaluated for this application. In the separation of the individual platinum metals from their ore, several schemes rely on the precipitation of [RhCl(NH3)5]Cl2. In some separation schemes, palladium is purified by manipulating equilibria involving [Pd(NH3)4]Cl2, PdCl2(NH3)2, and Pt(NH3)4[PdCl4]. In the processing of cellulose, the copper ammine complex known as Schweizer's reagent ([Cu(NH3)4(H2O)2](OH)2) is sometimes used to solubilise the polymer.
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He was the first to apply certain formal mathematical techniques to individual decision making in economics. He developed utility theory, introducing the indifference curve and the famous Edgeworth box, which is now familiar to undergraduate students of microeconomics. He is also known for the Edgeworth conjecture, which states that the core of an economy shrinks to the set of competitive equilibria as the number of agents in the economy gets larger. In statistics, Edgeworth is most prominently remembered by having his name on the Edgeworth series.
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The one-sector OLG model was further augmented with the introduction of a two- sector OLG model by Oded Galor. The two-sector model provides a framework of analysis for the study of the sectoral adjustments to aggregate shocks and implications of international trade for the dynamics of comparative advantage. In contrast to the Uzawa two-sector neoclassical growth model, the two-sector OLG model may be characterized by multiple steady-state equilibria, and initial conditions may therefore affect the long-run position of an economy.
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As part of Ostwald's investigations in to chemical equilibria, chemical affinity, and acid-base interactions, he recognized that many established analytical methods disturb the chemical systems under investigation. He therefore turned to physical measurements as surrogate methods to understand these important basic phenomena. One such physical measurement is the measurement of the viscosity, or resistance to flow, of a liquid. Ostwald invented a device for this purpose consisting of bulbs that act as reservoirs for a liquid with a capillary, or thin tube, in between the reservoirs.
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Levine also conducts research in the field of dynamic games. He established with Drew Fudenberg that a long-lived player playing in opposition to short- lived players can substitute reputation for commitment. He developed with Eric Maskin the first "folk theorem" for games in which players do not directly observe each other's decisions, with applications for learning in games. They argued that while learning theories cannot provide detailed descriptions of non-equilibrium behavior, they act as a useful tool in understanding which equilibria are likely to emerge.
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It is a tetrahedral species of idealized symmetry C3v with As-O bond lengths ranging from 1.66 to 1.71 Å. Being a triprotic acid, its acidity is described by three equilibria: :H3AsO4 \+ H2O + H3O+ (pKa1 = 2.19) : + H2O + H3O+ (pKa2 = 6.94) : + H2O + H3O+ (pKa3 = 11.5) These pKa values are close to those for phosphoric acid. The highly basic arsenate ion () is the product of the third ionization. Unlike phosphoric acid, arsenic acid is an oxidizer, as illustrated by its ability to convert iodide to iodine.
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However, also strong workers' rights and a technology characterized by a high intensity of highly specific labor can be institutional complements and define an alternative organizational equilibrium. The organizational equilibria approach integrate the approach of Oliver Williamson,Williamson O E (1985) The economic institutions of capitalism. The Free Press, New York. which have pointed out the influence of technology on rights and safeguards, and the views of the Radical Economists,Braverman H (1974) Labor and monopoly capital: The degradation of work in the twentieth century.
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The change in structure is measured by calculating the root mean square deviation from the backbone atomal position of the favored structure. The structure of the foldamer under different conditions can be determined computationally and then verified experimentally. Changes in the temperature, solvent viscosity, pressure, pH, and salt concentration can all yield valuable information about the structure of the foldamer. Measuring the kinetics of folding as well as folding equilibria allow one to observe the effects of these different conditions on the foldamer structure.
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A. R. Schultz, P. J. Flory, Phase Equilibria in Polymer-Solvent Systems, Journal of the American Chemical Society, 1952, Volume 74, pp 4760–4767. Also desirable for many applications is a sharp phase transition, which is reflected by a sudden drop in transmittance. The sharpness of the phase transition is related to the extent of phase separation but additionally relies on whether all present polymer chains exhibit the same cloud point. This depends on the polymer endgroups, dispersity, or—in the case of copolymers—varying copolymer compositions.
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From 1935 to 1971 Darken was employed at U.S. Steel Corporation Research Laboratory where he was director of the Edgar C. Bain Laboratory for Fundamental Research. After his retirement from U.S. Steel in 1971, he was appointed professor of mineral science at Pennsylvania State University. In addition to his two equations on diffusion, Dr. Darken made contributions to the field with respect to chemical rate phenomena in liquid steel and slags, thermodynamics of metallic solutions, and phase equilibria in various ternary systems.Fisher R.M., R.A. Oriani, E.T. Turkdogan.
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The experimental determination of a pKa value is commonly performed by means of a titration. Chapter 4: Experimental Procedure for Potentiometric pH Measurement of Metal Complex Equilibria A typical procedure would be as follows. A quantity of strong acid is added to a solution containing the acid or a salt of the acid, to the point where the compound is fully protonated. The solution is then titrated with a strong base :HA + OH− → A− \+ H2O until only the deprotonated species, A−, remains in solution.
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Every finite extensive game with perfect recall has a subgame perfect equilibrium. A common method for determining subgame perfect equilibria in the case of a finite game is backward induction. Here one first considers the last actions of the game and determines which actions the final mover should take in each possible circumstance to maximize his/her utility. One then supposes that the last actor will do these actions, and considers the second to last actions, again choosing those that maximize that actor's utility.
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Pliska–Pinheiro–Pinto Optimization paper determined the optimal life insurance purchase in a continuous-time model where the individual's lifetime is modeled through the concept of uncertain lifetime found in reliability theory. Pinto–Pinheiro–Yannacopoulos's JDEA paper study price formation in the Arrow–Debreu financial models with multiple assets from an unconventional perspective using Edgeworthian exchange models. Pinto–Pinheiro–Yannacopoulos's JDEA paper develops a stochastic model for the dynamics of bargaining. Araujo–-Choubdar-Maldonado–Pinheiro–Pinto proved the stochastic stability of sunspot equilibria in some specific cases.
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For the equation of state VTPR needs the critical temperature and pressure and additionally at least the acentric factor for all pure components in the considered mixture. A better quality can be achieved if the acentric factor is replaced by Twu constants which have been fitted to experimal vapor pressure data of pure components. The mixing rule uses UNIFAC which needs a variety of UNIFAC-specific parameters. Beside some model constants the most important are group interaction parameters which are fitted to experimental vapor–liquid equilibria of mixtures.
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The trialkylaluminium dimers often participate in dynamic equilibria, resulting in the interchange of bridging and terminal ligands as well as ligand exchange between dimers. Even in noncoordinating solvents, Al-Me exchange is fast, as confirmed by proton NMR spectroscopy. For example, at −25 °C the 1H NMR spectrum of Me6Al2 comprises two signals in 1:2 ratio, as expected from the solid state structure. At 20 °C, only one signal is observed because exchange of terminal and bridging methyl groups is too fast to be resolved by NMR.
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One of the principal uses of the notion of a subgame is in the solution concept subgame perfection, which stipulates that an equilibrium strategy profile be a Nash equilibrium in every subgame. In a Nash equilibrium, there is some sense in which the outcome is optimal - every player is playing a best response to the other players. However, in some dynamic games this can yield implausible equilibria. Consider a two-player game in which player 1 has a strategy S to which player 2 can play B as a best response.
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Hotelling made pioneering studies of non-convexity in economics. In economics, non-convexity refers to violations of the convexity assumptions of elementary economics. Basic economics textbooks concentrate on consumers with convex preferences and convex budget sets and on producers with convex production sets; for convex models, the predicted economic behavior is well understood. When convexity assumptions are violated, then many of the good properties of competitive markets need not hold: Thus, non-convexity is associated with market failures, where supply and demand differ or where market equilibria can be inefficient.
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Since 1988, Wong-Ng works as a research chemist in the ceramics division at the National Institute of Standards and Technology. She served as president the Association of NIST Asian Pacific Americans from 2000 to 2003. Wong-Ng's research interest includes materials for energy applications, thermoelectric standards, metrology, and data, sorbent materials for sustainability, and high throughput combinatorial approach for novel materials discovery and property optimization for energy conversion applications. She also researches crystallography, phase equilibria, and crystal chemistry of energy materials to understand their structure and property relationships.
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Path dependence is when the decisions presented to people are dependent on prior decisions or experiences made in the past.Definition from "Our Love Of Sewers: A Lesson in Path Dependence", Dave Praeger, 15 June 2008. In economics and the social sciences, path dependence refers to either the outcomes at a single point in time, or to long-run equilibria of a process. In common usage, the phrase implies either: In the first usage, (A), "history matters" is trivially true in many contexts; everything has causes, and sometimes different causes lead to different outcomes.
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Path dependence theory was originally developed by economists to explain technology adoption processes and industry evolution. The theoretical ideas have had a strong influence on evolutionary economics. There are many models and empirical cases where economic processes do not progress steadily toward some pre-determined and unique equilibrium, but rather the nature of any equilibrium achieved depends partly on the process of getting there. Therefore, the outcome of a path-dependent process will often not converge towards a unique equilibrium, but will instead reach one of several equilibria (sometimes known as absorbing states).
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The blue line for the formation of is approximately horizontal, since the reaction C(s) + (g) → (g) leaves the number of moles of gas unchanged so that ΔS is small. As with any chemical reaction prediction based on purely thermodynamic grounds, a spontaneous reaction may be very slow if one or more stages in the reaction pathway have very high activation energies EA. If two metals are present, two equilibria have to be considered. The oxide with the more negative ΔG will be formed and the other oxide will be reduced.
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If all the players are playing the strategies in a Nash equilibrium, they have no unilateral incentive to deviate, since their strategy is the best they can do given what others are doing. The payoffs of the game are generally taken to represent the utility of individual players. A prototypical paper on game theory in economics begins by presenting a game that is an abstraction of a particular economic situation. One or more solution concepts are chosen, and the author demonstrates which strategy sets in the presented game are equilibria of the appropriate type.
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In his exposition of his scheme of closed system equilibrium thermodynamics, C. Carathéodory initially postulates that experiment reveals that a definite number of real variables define the states that are the points of the manifold of equilibria. In the words of Prigogine and Defay (1945): "It is a matter of experience that when we have specified a certain number of macroscopic properties of a system, then all the other properties are fixed."Prigogine, I., Defay, R. (1950/1954), p. 1.Silbey, R.J., Alberty, R.A., Bawendi, M.G. (1955/2005), p. 4.
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Brewer spent the first ten years of his life with his family in Youngstown, Ohio, where his father worked as a shoe repairman. In 1929, in the wake of the Great Depression, his family moved to Los Angeles, California. It was only six years later that Brewer decided to attend the California Institute of Technology. As an undergraduate at Caltech, Leo Brewer was strongly influenced by Professors E. Swift and D. Yost, and had his first taste of research studying equilibria and kinetics of olefin hydration under Professors D. Pressman and H. J. Lucas.
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In games with mixed-strategy Nash equilibria, the probability of a player choosing any particular (so pure) strategy can be computed by assigning a variable to each strategy that represents a fixed probability for choosing that strategy. In order for a player to be willing to randomize, their expected payoff for each (pure) strategy should be the same. In addition, the sum of the probabilities for each strategy of a particular player should be 1. This creates a system of equations from which the probabilities of choosing each strategy can be derived.
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It considers the special case where the long-run stable equilibrium can be identified as the minimum of a smooth, well-defined potential function (Lyapunov function). Small changes in certain parameters of a nonlinear system can cause equilibria to appear or disappear, or to change from attracting to repelling and vice versa, leading to large and sudden changes of the behaviour of the system. However, examined in a larger parameter space, catastrophe theory reveals that such bifurcation points tend to occur as part of well-defined qualitative geometrical structures.
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Reprinted (2000) Fed Res Bank Mn Q Rev 24 (1), 14–23 Diamond and Dybvig demonstrate that when banks provide pure demand deposit contracts, we can actually have multiple equilibria. If confidence is maintained, such contracts can actually improve on the competitive market outcome and provide better risk sharing. In such an equilibrium, a depositor will only withdraw when it is appropriate for him to do so under optimal risk-sharing. However, if agents panic, their incentives are distorted and in such an equilibrium, all depositors withdraw their deposits.
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All of these games are coordination games where equilibrium selection is an important problem. In these games one player has a preferred equilibrium, and one might suppose that the order of moves introduces an asymmetry that solves the coordination problem. In order to resolve this problem Weber, Camerer, and Knez (2004) study a coordination game where no player prefers one equilibrium over another. They find that in this game introducing order results in different equilibria being selected, and they conclude that MAPNASH may be an important predictive tool.
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In other words, he takes an action only if he prefers the situation in which his action is 'universalized.' A Kantian equilibrium is a vector of labor offers such that no player would like to multiply all offers by any non-negative number. This captures a kind of cooperation—agents do not contemplate deviating independently of others, but only in concert with others. In Roemer (2011), it is shown that, in a variety of games, Kantian equilibria deliver Pareto efficient allocations—they rectify the inefficiencies associated with Nash equilibrium.
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As a result, the movement of molecules through a metabolic network is governed by simple chemical equilibria (at reversible steps), with specific key enzymes that are subject to regulation (at irreversible steps). This enzymatic regulation may be indirect, in the case of an enzyme being regulated by some cell signalling mechanism (like phosphorylation), or it may be direct, as in the case of allosteric regulation, where metabolites from a different portion of a metabolic network bind directly to and affect the catalytic function of other enzymes in order to maintain homeostasis.
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Cheap talk can, in general, be added to any game and has the potential to enhance the set of possible equilibrium outcomes. For example, one can add a round of cheap talk in the beginning of the Battle of the Sexes. Each player announces whether they intend to go to the football game, or the opera. Because the Battle of the Sexes is a coordination game, this initial round of communication may enable the players to select among multiple equilibria, thereby achieving higher payoffs than in the uncoordinated case.
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Jürgen Nührenberg (born February 2, 1942 in Berlin) is a German plasma physicist. Nührenberg studied physics at the University of Göttingen and the Ludwig Maximilian University of Munich, where he received his doctorate from in 1969 (translated: Linear and Toroidal Magnetohydrostatic Equilibria). He was a post-doctoral student at the University of Iowa and the Courant Institute of Mathematical Sciences of New York University. In 1971, he worked at the Max Planck Institute for Plasma Physics (IPP) in Garching near Munich, where he dealt with the theory of stellarators for controlled nuclear fusion.
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Ole Kleppa also made a unique contribution to the field of molten salts, as his measurements and methods gave rise to great progress in the field. Kleppa served as the Associate Director of the James Franck Institute from 1968 to 1971 and then its Director from 1971 to 1977. He also served as Director of the Materials Research Lab at the University of Chicago from 1984 to 1987. During his career, he held positions on the board of editors of the Journal of Chemical Thermodynamics, Journal of Physical Chemistry, and Journal of Phase Equilibria.
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This, of course, means defection at the first stage. In the Nash equilibria, however, the actions that would be taken after the initial choice opportunities (even though they are never reached since the first player defects immediately) may be cooperative. Defection by the first player is the unique subgame perfect equilibrium and required by any Nash equilibrium, it can be established by backward induction. Suppose two players reach the final round of the game; the second player will do better by defecting and taking a slightly larger share of the pot.
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1086 is a semi-empirical system for the prediction of non- electrolyte activity in non-ideal mixtures. UNIFAC uses the functional groups present on the molecules that make up the liquid mixture to calculate activity coefficients. By using interactions for each of the functional groups present on the molecules, as well as some binary interaction coefficients, the activity of each of the solutions can be calculated. This information can be used to obtain information on liquid equilibria, which is useful in many thermodynamic calculations, such as chemical reactor design, and distillation calculations.
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The best known of these papers is the 1978 Econometrica article cited, which establishes by elementary means a very general theorem on the cores of exchange economies. In the 2008 Econometrica article cited, Anderson and Raimondo provide the first satisfactory proof of existence of equilibrium in a continuous-time securities market with more than one agent. The paper also provides a convergence theorem relating the equilibria of discrete-time securities markets to those of continuous-time securities markets. It uses Anderson’s nonstandard construction of Brownian and properties of real analytic functions.
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Furthermore, states near such thermal equilibria can be more easily controlled experimentally and departures from equilibrium studied with precision. When a neutral plasma is cooled, it simply recombines; but a plasma with a single sign of charge can be cooled without recombination. Malmberg constructed a trap for a pure electron plasma with walls at 4.2 K. Cyclotron radiation from the electrons then cooled the plasma to a few Kelvin. Theory argued that electron-electron collisions in such a strongly magnetized and low temperature plasma would be qualitatively different than those in warmer plasmas.
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The halide preference, coupled to the position of the two reaction equilibria allows for a nett transhalogenation reaction to be catalysed by the enzyme. Incubation of 5'-chloro nucleosides with the enzyme, along with catalytic L-selenomethionine or L-methionine results in the production of 5-fluoro nucleosides. When [18F]fluoride is used, this transhalogenation reaction can be used for the synthesis of radiotracers for positron emission tomography. Incubation of ClDA with the fluorinase in the presence of L-methionine and fluoride ion results in the generation of FDA, through a SAM intermediate.
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The sexual interference hypothesis proposes that additional male signals evolve to hinder female mate choice by interfering with the propagation and reception of other males' sexual signals. Females respond by evolving the ability to glean meaningful information from signals despite males' attempts at obfuscation. In turn, males respond by producing better interference signals and new signals that are not so easily blocked. This iterative coevolutionary process increases the costs of assessment for females and the costs of signal production for males, and leads to temporary equilibria of honest advertising via multiple signals.
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For experimental physics, hotness means that, when comparing any two given bodies in their respective separate thermodynamic equilibria, any two suitably given empirical thermometers with numerical scale readings will agree as to which is the hotter of the two given bodies, or that they have the same temperature.Beattie, J.A., Oppenheim, I. (1979). Principles of Thermodynamics, Elsevier Scientific Publishing Company, Amsterdam, , p. 29. This does not require the two thermometers to have a linear relation between their numerical scale readings, but it does require that the relation between their numerical readings shall be strictly monotonic.
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Examples of topics covered by the ASM Handbooks are mechanical properties of metals, corrosion studies, and much more. Other publications include technical journals such as Metallurgical and Materials Transactions A and Journal of Phase Equilibria and Diffusion. ASM also hosts numerous international conferences each year. Five affiliate societies focused on specific areas of materials science also fall under the ASM umbrella: The Heat Treating Society (HTS), the Thermal Spray Society (TSS), the International Metallographic Society (IMS), the Electronic Device Failure Analysis Society (EDFAS), and Shape Memory and Superelastic Technology (SMST).
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Beta is also sometimes used when discussing the interaction of plasma in space with different magnetic fields. A common example is the interaction of the solar wind with the magnetic fields of the SunAlan Hood, "The Plasma Beta", Magnetohydrostatic Equilibria, 11 January 2000 or Earth.G. Haerendel et all, "High-beta plasma blobs in the morningside plasma sheet", Annales Geophysicae, Volume 17 Number 12, pg. 1592-1601 In this case, the betas of these natural phenomena are generally much smaller than those seen in reactor designs; the Sun's corona has a beta around 1%.
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His later studies centred mainly on the theory of differentiable economies, where he showed that, in general, aggregate excess demand functions vanish at a finite number of points – basically, he showed that economies have a finite number of price equilibria. In 1976, he received the French Legion of Honour. He was awarded the 1983 Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel, for having incorporated new analytical methods into economic theory and for his rigorous reformulation of general equilibrium theory. He was a member of the International Academy of Science.
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The Stackelberg model can be solved to find the subgame perfect Nash equilibrium or equilibria (SPNE), i.e. the strategy profile that serves best each player, given the strategies of the other player and that entails every player playing in a Nash equilibrium in every subgame. In very general terms, let the price function for the (duopoly) industry be P; price is simply a function of total (industry) output, so is P(q_1+q_2) where the subscript 1 represents the leader and 2 represents the follower. Suppose firm i has the cost structure C_i(q_i).
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Importantly, Milton Friedman himself never wrote down an explicit model of the natural rate (in his Nobel Lecture, he just uses the simple labor supply and demand model). Others have argued that there might be multiple equilibria: for example due to search externalities as in the Diamond coconut model or that there might exist a "natural range" of unemployment levels rather than a unique equilibrium. According to Roger Farmer of UCLA, the assumption that, after a shock, the unemployment rate returns to its so called “natural rate' does not hold in the data.
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Fig. 12. Price lines for a box with boundary equilibriaKenneth Arrow and Gérard Debreu published papers independently in 1951 drawing attention to limitations in the calculus proofs of equilibrium theorems.K. Arrow, ‘An Extension of the Basic Theorems of Classical Welfare Economics’ (1951); G. Debreu, ‘The Coefficient of Resource Utilization’ (1951). Arrow specifically mentioned the difficulty caused by equilibria on the boundary, and Debreu the problem of non- differentiable indifference curves. Without aiming for exhaustive coverage it is easy to see in intuitive terms how to extend our methods to apply to these cases.
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Hong's research focuses on elucidating the structure, dynamics and mechanism of membrane proteins using ssNMR. She is particularly known for her in-depth study of the Matrix-2 (M2) proteins of influenza A viruses, which are responsible for all flu pandemics in history. M2 is an acid-activated proton channel and a membrane scission protein of the influenza virus. Hong's ssNMR studies have provided insights into the proton-conduction mechanism of this channel, by quantifying the proton transfer rates and equilibria between water and the proton-selective histidine residue.
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This principle of mobile equilibrium was subsequently (1885) put in a general form by Henry Louis Le Chatelier, who extended the principle to include compensation, by change of volume, for imposed pressure changes. The van 't Hoff-Le Chatelier principle, or simply Le Chatelier's principle, explains the response of dynamic chemical equilibria to external stresses. In 1884, Hermann Emil Fischer proposed the structure of purine, a key structure in many biomolecules, which he later synthesized in 1898. He also began work on the chemistry of glucose and related sugars.
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Economics is closely enough linked to optimization of agents that an influential definition relatedly describes economics qua science as the "study of human behavior as a relationship between ends and scarce means" with alternative uses.Lionel Robbins (1935, 2nd ed.) An Essay on the Nature and Significance of Economic Science, Macmillan, p. 16. Modern optimization theory includes traditional optimization theory but also overlaps with game theory and the study of economic equilibria. The Journal of Economic Literature codes classify mathematical programming, optimization techniques, and related topics under JEL:C61-C63.
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In game theory, folk theorems are a class of theorems describing an abundance of Nash equilibrium payoff profiles in repeated games .In mathematics, the term folk theorem refers generally to any theorem that is believed and discussed, but has not been published. Roger Myerson has recommended the more descriptive term "general feasibility theorem" for the game theory theorems discussed here. See Myerson, Roger B. Game Theory, Analysis of conflict, Cambridge, Harvard University Press (1991) The original Folk Theorem concerned the payoffs of all the Nash equilibria of an infinitely repeated game.
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Global coordination games belong to a subfield of game theory that gained momentum in 1998 when he published an article with Stephen Morris. Shin and Morris considered a stylized currency crises model, in which traders observe the relevant fundamentals with small noise, and show that this leads to the selection of a unique equilibrium. This result is in stark contrast with models of complete information, which feature multiple equilibria. In 2011 he won the second Financial Times annual essay contest on banking regulation sponsored by the International Centre for Financial Regulation.
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In general nondegenerate cases, there can be at most one interior evolutionary stable state (ESS), though there can be many equilibria on the boundary of the simplex. All the faces of the simplex are forward-invariant which corresponds to the lack of innovation in the replicator equation: once a strategy becomes extinct there is no way to revive it. Phase portrait solutions for the continuous linear- fitness replicator equation have been classified in the two and three dimensional cases. Classification is more difficult in higher dimensions because the number of distinct portraits increases rapidly.
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Cass's last published paper was "Compatible beliefs and equilibrium" (2008, J. Math. Econ. 44, 625-640) Cass describes this paper as a concept paper, in which he goes back to the primitives of economic theory and asks what beliefs economic agents must hold in order to justify the conventional assumption of competitive equilibrium. Cass's last paper, "Utility-based utility" was under revision at the time of his death. This paper is also conceptual in nature in showing that sunspot equilibria could exist under weaker specifications of preferences than the standard von Neumann-Morgenstern specification.
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Nobel Prize certificate for Wilhelm Ostwald Ostwald received the 1909 Nobel Prize for Chemistry for his contributions to understanding catalysis and for his investigations of the fundamental principles underlying chemical equilibria and reaction rates. He was nominated for the Nobel Prize 20 times beginning in 1914, and he submitted nine nominations of other scientists for the Nobel Prize following his own award. This included two nominations of Albert Einstein. Ostwald, donated more than US$40,000 of his Nobel Prize award money to advance the cause of the Ido language.
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Since almost all adsorptive separation processes are dynamic -meaning, that they are running under flow - testing porous materials for those applications for their separation performance has to be tested under flow as well. Since separation processes run with mixtures of different components, measuring several breakthrough curves results in thermodynamic mixture equilibria - mixture sorption isotherms, that are hardly accessible with static manometric sorption characterization. This enables the determination of sorption selectivities in gaseous and liquid phase. The determination of breakthrough curves is the foundation of many other processes, like the pressure swing adsorption.
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A novel synthetic pathway to vitisin B compounds. Joana Oliveira, Victor de Freitas and Nuno Mateus, Tetrahedron Letters, Volume 50, Issue 27, 8 July 2009, Pages 3933-3935, Charge equilibria and pK values of 5-carboxypyranomalvidin-3-glucoside (vitisin A) by electrophoresis and absorption spectroscopy. Robert E. Asenstorfer and Graham P. Jones, Tetrahedron, Volume 63, Issue 22, 28 May 2007, Pages 4788-4792, Effect of acetaldehyde and several acids on the formation of vitisin A in model wine anthocyanin and colour evolution. Romero C. and Bakker J., International journal of food science & technology, 2000, vol.
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Human factors are the physical or cognitive properties of individuals, or social behavior which is specific to humans, and influence functioning of technological systems as well as human-environment equilibria. The safety of underwater diving operations can be improved by reducing the frequency of human error and the consequences when it does occur. Human error can be defined as an individual's deviation from acceptable or desirable practice which culminates in undesirable or unexpected results. > Dive safety is primarily a function of four factors: the environment, > equipment, individual diver performance and dive team performance.
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Using the resources of Cornell and those of various funding agencies he built a vibrant international collaborative laboratory in statistical mechanics and molecular modelling, to which he welcomed many international visiting scientists. It was while at Cornell that he teamed up with a fellow faculty member, William ('Bill') B. Streett, an internationally renowned expert in high-pressure phase equilibria and molecular simulation of fluids. It was from Bill that he learned about the potential of molecular simulation methods. Together they formed a successful joint program involving experimental and theoretical studies of liquid mixtures.
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Perakis has received numerous awards and distinctions over the course of her career, including the 2000 National Science Foundation CAREER Award, the 2000 PECASE Award (Presidential Early Career Award for Scientists and Engineers) for her "outstanding research on the development of a theory for understanding the nature of traffic equilibria, and for her commitment to undergraduate and graduate education," and Faculty awards by Adobe in 2017 and IBM in 2015 and 2016. In 2016, she was elected as a Fellow of INFORMS, the highest honor of the largest society of analytics professionals.
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Coordination games also have mixed strategy Nash equilibria. In the generic coordination game above, a mixed Nash equilibrium is given by probabilities p = (d-b)/(a+d-b-c) to play Up and 1-p to play Down for player 1, and q = (D-C)/(A+D-B-C) to play Left and 1-q to play Right for player 2. Since d > b and d-b < a+d-b-c, p is always between zero and one, so existence is assured (similarly for q). The reaction correspondences for 2×2 coordination games are shown in Fig. 6.
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The first consequence of such a requirement is that budget sets do not fill the available space and are typically smaller than hyperplanes. Because the dimension of vectors orthogonal to the budget set is larger than one there is no reason for the price systems supporting an equilibrium to be unique up to scaling, likewise the first order conditions no longer implies that gradient of agents are collinear at equilibrium. Both happen to fail to hold generically: the first theorem of welfare economics is hence the first victim of incompleteness. Pareto-optimality of equilibria generally does not hold.
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Mikhail Mikhaylovich Shultz (, also spelled Schultz, Shul'ts, Shults, Shul’c etc.) (1 July 1919 – 9 October 2006), was a Soviet/Russian physical chemist, artist. Proceedings of the thermodynamic theory, the thermodynamics of heterogeneous systems, the theory of glasses, chemistry and electrochemistry of glass, membrane electrochemistry, the theory of ion exchange and phase equilibria of multicomponent systems, the theory of glass electrode. The name of the scientist linked the formation of pH-meters and ionometry, production organisation, instrumentation and materials commonly used in medicine, chemical and nuclear industry, aviation rocket and space technology, agriculture and many other areas.
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His work was continued by Walther Nernst, who derived the Nernst equation and described ionic conduction in heterovalently doped zirconia, which he used in his Nernst lamp. Nernst was inspired by the dissociation theory of Arrhenius published in 1887, which relied on ions in solution. In 1889 he realized the similarity between electrochemical and chemical equilibria, and formulated his famous equation that correctly predicted the output voltage of various electrochemical cells based on liquid electrolytes from the thermodynamic properties of their components. Besides his theoretical work, in 1897 Nernst patented the first lamp that used a solid electrolyte.
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At typical ambient temperatures, sodium hypochlorite is more stable in dilute solutions that contain solvated and ions. The density of the solution is 1.093 g/mL at 5% concentration, and 1.21 g/mL at 14%, 20 °C.Environment Canada (1985): "Tech Info for Problem Spills: Sodium Hypochlorite (Draft)". Stoichiometric solutions are fairly alkaline, with pH 11 or higher since hypochlorous acid is a weak acid: : + HOCl + The following species and equilibria are present in solutions of : : (aq) ⇌ + : (aq) + + ⇌ (aq) + : (aq) + ⇌ : (aq) ⇌ (g) The second equilibrium equation above will be shifted to the right if the chlorine is allowed to escape as gas.
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It has applications in all fields of social science, as well as in logic, systems science and computer science. Originally, it addressed zero-sum games, in which each participant's gains or losses are exactly balanced by those of the other participants. In the 21st century, game theory applies to a wide range of behavioral relations, and is now an umbrella term for the science of logical decision making in humans, animals, and computers. Modern game theory began with the idea of mixed-strategy equilibria in two-person zero-sum games and its proof by John von Neumann.
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The government's payoff here is not modeled explicitly, and the amount of foreign reserves the can be used for defending exchange rate is given. More realistically, the tenacity with which the exchange rate is defended depends on a variety of factors in the domestic economy, and the government will optimally choose the limit of defending. The no attack equilibrium Pareto dominates the attack equilibrium, which means in the attack equilibrium every player is worse off compared to the no attack equilibrium. The economic inefficiency results from lack of coordination among the investors, and the existence of multiple equilibria makes the bad equilibrium possible.
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The mechanism of self- fulfilling crisis depends crucially on the multiplicity of equilibria. In Morris and Shin (1998), the authors assumed that the economic fundamentals are not common knowledge to all the agents, and investors have access to heterogeneous information about the economic condition, then there will be some uncertainty about equilibrium, and speculators are uncertain about what other spectators will do. As a result, their model achieves the uniqueness of equilibrium.Morris, Stephen and Hyun Song Shin (1998), Unique Equilibrium in a Model of Self-Fulfilling Currency Attacks, American Economic Review 88(3), pp. 587–597.
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Separately, game theory has played a role in online algorithms; in particular, the -server problem, which has in the past been referred to as games with moving costs and request- answer games. Yao's principle is a game-theoretic technique for proving lower bounds on the computational complexity of randomized algorithms, especially online algorithms. The emergence of the Internet has motivated the development of algorithms for finding equilibria in games, markets, computational auctions, peer-to-peer systems, and security and information markets. Algorithmic game theory and within it algorithmic mechanism design combine computational algorithm design and analysis of complex systems with economic theory.
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COSMOSPACE (COSMO Surface-Pair Activity Coefficient Equation) is an activity coefficient model in which the activity coefficient of the components in a liquid chemical mixture can be related through their molar fraction.Andreas Klamt, Gerard J. P. Krooshof, Ross Taylor "COSMOSPACE: Alternative to conventional activity-coefficient models", AIChE J., 48(10), 2332–2349, (2002) It was initially developed as an implicit solution to COSMO-RS. While UNIQUAC is a first order approximation, COSMOSPACE gives the exact solution of a lattice model in which pairwise molecule surfaces interact. Therefore, COSMOSPACE outperforms Uniquac in the description of vapor–liquid and liquid–liquid phase equilibria.
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A slotted Aloha wireless network employs the Aloha MAC protocol where the channels access the medium, independently at each time interval, with some probability p. If the underlying channels (that is, their transmitters for the point-to-point case) are positioned according to a Poisson process (with density λ), then the nodes accessing the network also form a Poisson network (with density pλ), which allows the use of the Poisson model. ALOHA is not only one of the simplest and most classic MAC protocol but also was shown to achieve Nash equilibria when interpreted as a power control schemes.X. Zhang and M. Haenggi.
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For most planets, the rotation period and axial tilt (also called obliquity) are not known, but a large number of planets have been detected with very short orbits (where tidal effects are greater) that will probably have reached an equilibrium rotation that can be predicted (i.e. tidal lock, spin–orbit resonances, and non-resonant equilibria such as retrograde rotation). Gravitational tides tend to reduce the axial tilt to zero but over a longer timescale than the rotation rate reaches equilibrium. However, the presence of multiple planets in a system can cause axial tilt to be captured in a resonance called a Cassini state.
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Each interbreeding group will rapidly develop its own characteristic appearance. An individual from one group which wanders into another group will consequently be recognized as different, and will be discriminated against during the mating season. Reproductive isolation induced by koinophilia might thus be the first crucial step in the development of, ultimately, physiological, anatomical and behavioral barriers to hybridization, and thus, ultimately, full specieshood. Koinophilia will thereafter defend that species' appearance and behavior against invasion by unusual or unfamiliar forms (which might arise by immigration or mutation), and thus be a paradigm of punctuated equilibria (or the "vertical" aspect of the speciation problem).
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After the publication of MELTS, Ghiorso continued to improve and extend it with the help of colleagues such as Mark Hirschmann, Paul Asimow, Pete Reiners and Victor Kress. After they identified some fundamental problems with the theory at high pressure, they developed pMELTS, a model for high pressures (1-3 gigapascals (GPa)), and published it in 2001. Asimow and co- authors published phMELTS, a model for mid-ocean ridge basalts that incorporated the effect of water content. In 1998, Ghiorso, Hirschmann and Tim Grove established the Library of Experimental Phase Relations (LEPR), an online database for experimental results on solid-melt equilibria.
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A nonlinear dynamical system exhibits chaotic hysteresis if it simultaneously exhibits chaotic dynamics (chaos theory) and hysteresis. As the latter involves the persistence of a state, such as magnetization, after the causal or exogenous force or factor is removed, it involves multiple equilibria for given sets of control conditions. Such systems generally exhibit sudden jumps from one equilibrium state to another (sometimes amenable to analysis using catastrophe theory). If chaotic dynamics appear either prior to or just after such jumps, or are persistent throughout each of the various equilibrium states, then the system is said to exhibit chaotic hysteresis.
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One result states that under mild assumptions the number of equilibria will be finite (see regular economy) and odd (see index theorem). Furthermore, if an economy as a whole, as characterized by an aggregate excess demand function, has the revealed preference property (which is a much stronger condition than revealed preferences for a single individual) or the gross substitute property then likewise the equilibrium will be unique. All methods of establishing uniqueness can be thought of as establishing that each equilibrium has the same positive local index, in which case by the index theorem there can be but one such equilibrium.
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In a typical general equilibrium model the prices that prevail "when the dust settles" are simply those that coordinate the demands of various consumers for various goods. But this raises the question of how these prices and allocations have been arrived at, and whether any (temporary) shock to the economy will cause it to converge back to the same outcome that prevailed before the shock. This is the question of stability of the equilibrium, and it can be readily seen that it is related to the question of uniqueness. If there are multiple equilibria, then some of them will be unstable.
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It becomes smaller, and the larger balloon becomes larger. The air flow ceases when the two balloons have equal pressure, with one on the left branch of the pressure curve (rp) and one on the right branch (r>rp). Equilibria are also possible in which both balloons have the same size. If the total quantity of air in both balloons is less than Np, defined as the number of molecules in both balloons if they both sit at the peak of the pressure curve, then both balloons settle down to the left of the pressure peak with the same radius, rp.
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Sometimes subgame perfection does not impose a large enough restriction on unreasonable outcomes. For example, since subgames cannot cut through information sets, a game of imperfect information may have only one subgame – itself – and hence subgame perfection cannot be used to eliminate any Nash equilibria. A perfect Bayesian equilibrium (PBE) is a specification of players’ strategies and beliefs about which node in the information set has been reached by the play of the game. A belief about a decision node is the probability that a particular player thinks that node is or will be in play (on the equilibrium path).
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Coordination failure is another potential explanation for recessions and unemployment. In recessions a factory can go idle even though there are people willing to work in it, and people willing to buy its production if they had jobs. In such a scenario, economic downturns appear to be the result of coordination failure: The invisible hand fails to coordinate the usual, optimal, flow of production and consumption. Russell Cooper and Andrew John (1988) expressed a general form of coordination as models with multiple equilibria where agents could coordinate to improve (or at least not harm) each of their respective situations.
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Eldredge & Gould (1972) took Mayr's model of allopatric speciation and combined it with Wright's model of genetic drift in order to explain gaps in the fossil record as results of relatively swift evolutionary change in small and isolated populations. Although catastrophes can produce such populations they are not required, and the mechanism underlying the punctuated record is the drift within small and isolated populations, not the absence of competing species that would prevent species transmutation. Therefore, viewing Matthew (1831) as an anticipator of the theory of punctuated equilibria (e.g. Rampino, 2011) is as wrong as claiming his scheme identical to Darwin's or Wallace's.
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If, at the end of the process, there is a single strategy for each player, this strategy set is also a Nash equilibrium. However, unlike the first process, elimination of weakly dominated strategies may eliminate some Nash equilibria. As a result, the Nash equilibrium found by eliminating weakly dominated strategies may not be the only Nash equilibrium. (In some games, if we remove weakly dominated strategies in a different order, we may end up with a different Nash equilibrium.) Weak Dominance Deletion Step-by-Step Example: frameless # O is strictly dominated by N for Player 1.
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His research focused on trace metals in natural waters, particularly in the ocean, and chemical equilibria in marine and freshwater systems. He found that the productivity of phytoplankton in much of the oceans is limited by the availability of iron. Hunter served a term as president of the New Zealand Institute of Chemistry, and was involved in the establishment of the NIWA/University of Otago Joint Institute for Oceanography in 1996. He was awarded the Prime Minister's Science Prize in 2011 and the Marsden Medal in 2014, and was elected a Fellow of the Royal Society of New Zealand in 1997.
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Thomas Rossman Palfrey (born 1953) is the Flintridge Professor of Economics and Political Science at the California Institute of Technology (Caltech) in Pasadena, California, and Fellow of the Econometric Society. He received his Ph.D in Social Science from Caltech in 1981. He has authored influential papers in the fields of political economy ("Voter Participation and Strategic Uncertainty" with Howard Rosenthal, APSR 1985), game theory ("Quantal Response Equilibria in Normal Form Games" with Richard McKelvey, GEB 1995), implementation ("Nash Implementation Using Undominated Strategies" with S. Srivastava, Econometrica 1991), and experimental economics ("An Experimental Study of the Centipede Game" with R. McKelvey, Econometrica 1992).
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The gas fugacity coefficients are mostly set to unity (ideal gas assumption), but for vapor-liquid equilibria at high pressures (i.e. > 10 bar) an equation of state is needed to calculate the gas fugacity coefficient for a real gas description. Determination of NRTL parameters from LLE data is more complicated than parameter regression from VLE data as it involves solving isoactivity equations which are highly non- linear. In addition, parameters obtained from LLE may not always represent the real activity of components due to lack of knowledge on the activity values of components in the data regression.
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The IS curve represents the locus where total spending (consumer spending + planned private investment + government purchases + net exports) equals total output (real income, Y, or GDP). The IS curve also represents the equilibria where total private investment equals total saving, with saving equal to consumer saving plus government saving (the budget surplus) plus foreign saving (the trade surplus). The level of real GDP (Y) is determined along this line for each interest rate. Every level of the real interest rate will generate a certain level of investment and spending: lower interest rates encourage higher investment and more spending.
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The players in a game are playing a Berge equilibrium if they have chosen a strategy profile such that, if any given player i sticks with their chosen strategy while some of the other players change their strategies, then player i's payoff will not increase. So, every player in a Berge equilibrium guarantees the best possible payoff for every other player who is playing their Berge equilibrium strategy; this is a contrast with Nash equilibria, in which each player i is only concerned about maximizing their own payoffs from their strategy, and no other player cares about the payoff obtained by player i.
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The software aqion is shipped with a set of example solutions (input waters) and a tutorial how to attack typical water-related problems (online-manual with about 40 examples). More examples and exercises for testing and re-run can be found in classical textbooks of hydrochemistry.Stumm, W. and J. J. Morgan: Aquatic Chemistry, Chemical Equilibria and Rates in Natural Waters (3rd ed.), John Wiley & Sons, Inc., New York, 1996, Morel, F. M. M. and J. G. Hering: Principles and Applications of Aquatic Chemistry (2nd ed.), John Wiley, New York, 1993, Appelo, C. A. J. and D. Postma: Geochemistry, Groundwater, and Pollution.
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In ecology, the theory of alternative stable states (sometimes termed alternate stable states or alternative stable equilibria) predicts that ecosystems can exist under multiple "states" (sets of unique biotic and abiotic conditions). These alternative states are non-transitory and therefore considered stable over ecologically-relevant timescales. Ecosystems may transition from one stable state to another, in what is known as a state shift (sometimes termed a phase shift or regime shift), when perturbed. Due to ecological feedbacks, ecosystems display resistance to state shifts and therefore tend to remain in one state unless perturbations are large enough.
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A knowledge of pKa values is important for the quantitative treatment of systems involving acid–base equilibria in solution. Many applications exist in biochemistry; for example, the pKa values of proteins and amino acid side chains are of major importance for the activity of enzymes and the stability of proteins. Protein pKa values cannot always be measured directly, but may be calculated using theoretical methods. Buffer solutions are used extensively to provide solutions at or near the physiological pH for the study of biochemical reactions; the design of these solutions depends on a knowledge of the pKa values of their components.
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In these games the mixing Nash is the ESS if there is no uncorrelated asymmetry, and the pure conditional Nash equilibria are ESSes when there is an uncorrelated asymmetry. The usual applied example of an uncorrelated asymmetry is territory ownership in the hawk-dove game. Even if the two players ("owner" and "intruder") have the same payoffs (i.e., the game is payoff symmetric), the territory owner will play Hawk, and the intruder Dove, in what is known as the 'Bourgeois strategy' (the reverse is also an ESS known as the 'anti-bourgeois strategy', but makes little biological sense).
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In 1995 he met Arnold at a major mathematics conference in Hamburg, where Arnold presented a plenary talk illustrating that most geometrical problems have four solutions or extremal points. In a personal discussion, however, Arnold questioned whether four is a requirement for mono-monostatic bodies and encouraged Domokos to seek examples with fewer equilibria. The rigorous proof of the solution can be found in references of their work. The summary of the results is that the three- dimensional homogeneous convex (mono-monostatic) body, which has one stable and one unstable equilibrium point, does exist and is not unique.
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After his PhD, he worked at the Princeton Plasma Physics Laboratory (on "Project Matterhorn"), where he was one of the leading theoretical physicists and remained until 1982. In 1982 he was Senior Technical Advisor in the theory group of General Atomics and simultaneously adjunct professor at the University of California, San Diego. He was the author of a series of works with John Johnson and Katherine Weimer on equilibria and instabilities in Tokamak and Stellarator plasmas in magnetohydrodynamics. With Johnson and Ray Grimm he developed the computer program PEST (Princeton Equilibrium and Stability in Tokamak's Code).
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These give rise to unsatisfactory equilibria, but more seriously, cause a loss of static stability when turning in one direction, and an increase in static stability in the opposite direction. Shilovsky encountered this problem with his road vehicle, which consequently could not make sharp left hand turns. Brennan and Scherl were aware of this problem, and implemented their balancing systems with pairs of counter rotating gyros, precessing in opposite directions. With this arrangement, all motion of the vehicle with respect to inertial space causes equal and opposite torques on the two gyros, and are consequently cancelled out.
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For the equation of state PSRK needs the critical temperature and pressure, additionally at a minimum the acentric factor for all pure components in the considered mixture is also required. The integrity of the model can be improved if the acentric factor is replaced by Mathias–Copeman constants fitted to experimental vapor- pressure data of pure components. The mixing rule uses UNIFAC, which needs a variety of UNIFAC-specific parameters. Aside from some model constants, the most important parameters are the group-interaction parameters — these are obtained from parametric fits to experimental vapor–liquid equilibria of mixtures.
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Further, the surface stress on a solid is a directional quantity (a stress tensor) while surface energy is scalar. Fifteen years after Gibbs, J.D. van der Waals developed the theory of capillarity effects based on the hypothesis of a continuous variation of density. He added to the energy density the term c ( abla \rho)^2, where c is the capillarity coefficient and ρ is the density. For the multiphase equilibria, the results of the van der Waals approach practically coincide with the Gibbs formulae, but for modelling of the dynamics of phase transitions the van der Waals approach is much more convenient.
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Recent research has shown that bounded rationality of individuals may influence the topology of the social networks that evolve among them. In particular, Kasthurirathna and Piraveenan have shown that in socio-ecological systems, the drive towards improved rationality on average might be an evolutionary reason for the emergence of scale-free properties. They did this by simulating a number of strategic games on an initially random network with distributed bounded rationality, then re-wiring the network so that the network on average converged towards Nash equilibria, despite the bounded rationality of nodes. They observed that this re-wiring process results in scale-free networks.
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The main result of the theorem is that all the mixed strategy equilibria of a given game can be purified using the same sequence of perturbed games. However, in addition to independence of the perturbations, it relies on the set of payoffs for this sequence of games being of full measure. There are games, of a pathological nature, for which this condition fails to hold. The main problem with these games falls into one of two categories: (1) various mixed strategies of the game are purified by different sequences of perturbed games and (2) some mixed strategies of the game involve weakly dominated strategies.
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She studied Geology at the Paris-Sud 11 University in Orsay, in the south of Paris. She took a PhD in 1987 at the Institute of Human Paleontology, a Foundation Prince Albert 1er of Monaco, associated with the Muséum national d'histoire naturelle (National Museum of Natural History) in Paris. Her PhD thesis was on human embryonic origins of permanent bipedalism, she is Accredited to Direct Research Cum Magna Laude since 2011. As paleontologist, her controversial views on human origins come from homeobox genes and punctated equilibria included in her work, whereas paradigm explains permanent bipedalism as the result of gradual post-natal adaptations from arboreal environment to open savanna.
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Morey studied chemistry at the University of Minnesota with a bachelor's degree in 1909 and was a member of the Geophysical Laboratory of Carnegie Institution in Washington, DC from 1912 until his retirement in 1953. He was Acting Director of the Laboratory from 1952 to 1953 before Philip H. Abelson replaced him.Biography at the Carnegie Institution He focused on experimental investigations of phase equilibria and thermodynamics of silicate melts with volatile components, such as water and carbon dioxide. In both WW I and WW II, Morey, as an expert on glass, was involved in the Laboratory's optical glassmaking projects for military equipment, such as rangefinders and gunsights.
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In both the Ricardian and H–O models, the comparative advantage theory is formulated for a 2 countries/2 commodities case. It can be extended to a 2 countries/many commodities case, or a many countries/2 commodities case. Adding commodities in order to have a smooth continuum of goods is the major insight of the seminal paper by Dornbusch, Fisher, and Samuelson. In fact, inserting an increasing number of goods into the chain of comparative advantage makes the gaps between the ratios of the labor requirements negligible, in which case the three types of equilibria around any good in the original model collapse to the same outcome.
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In the modified game, that strategy g is played with probability 1, and the other player will play his best response to g with probability 1. Consider the continuum of games in which B is continuously reduced to 0. There exists a path of Nash equilibria connecting the unique equilibrium of the modified game, to an equilibrium of G. The pure strategy g chosen to receive the bonus B corresponds to the initially dropped label. While the algorithm is efficient in practice, in the worst case the number of pivot operations may need to be exponential in the number of pure strategies in the game.
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This paved the way for more general theorems. In 1938, the Danish mathematical economist Frederik Zeuthen proved that the mathematical model had a winning strategy by using Brouwer's fixed point theorem. In his 1938 book Applications aux Jeux de Hasard and earlier notes, Émile Borel proved a minimax theorem for two-person zero-sum matrix games only when the pay-off matrix was symmetric and provides a solution to a non-trivial infinite game (known in English as Blotto game). Borel conjectured the non-existence of mixed-strategy equilibria in finite two-person zero-sum games, a conjecture that was proved false by von Neumann.
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In economics, non-convexity refers to violations of the convexity assumptions of elementary economics. Basic economics textbooks concentrate on consumers with convex preferences (that do not prefer extremes to in-between values) and convex budget sets and on producers with convex production sets; for convex models, the predicted economic behavior is well understood. When convexity assumptions are violated, then many of the good properties of competitive markets need not hold: Thus, non-convexity is associated with market failures, where supply and demand differ or where market equilibria can be inefficient. Non-convex economies are studied with nonsmooth analysis, which is a generalization of convex analysis.
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Recent research in economics has recognized non-convexity in new areas of economics. In these areas, non- convexity is associated with market failures, where equilibria need not be efficient or where no competitive equilibrium exists because supply and demand differ. Non-convex sets arise also with environmental goods (and other externalities),Pages 106, 110–137, 172, and 248: and with market failures, and public economics.Pages 63–65: Starrett discusses non-convexities in his textbook on public economics (pages 33, 43, 48, 56, 70–72, 82, 147, and 234–236): Non-convexities occur also with information economics, and with stock markets (and other incomplete markets).
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This later suggestion has been pursued by several philosophers since Lewis. Following game-theoretic account of conventions, Edna Ullmann-Margalit (1977) and Bicchieri (2006) have developed theories of social norms that define them as Nash equilibria that result from transforming a mixed-motive game into a coordination game. Game theory has also challenged philosophers to think in terms of interactive epistemology: what it means for a collective to have common beliefs or knowledge, and what are the consequences of this knowledge for the social outcomes resulting from the interactions of agents. Philosophers who have worked in this area include Bicchieri (1989, 1993), Skyrms (1990), and Stalnaker (1999).
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The thermodynamic formalism allows that a system may have contact with several other systems at once, which may or may not also have mutual contact, the contacts having respectively different permeabilities. If these systems are all jointly isolated from the rest of the world those of them that are in contact then reach respective contact equilibria with one another. If several systems are free of adiabatic walls between each other, but are jointly isolated from the rest of the world, then they reach a state of multiple contact equilibrium, and they have a common temperature, a total internal energy, and a total entropy.Carathéodory, C. (1909).
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The image to the right shows a simple sequential game that illustrates the issue with subgame imperfect Nash equilibria. In this game player one chooses left(L) or right(R), which is followed by player two being called upon to be kind (K) or unkind (U) to player one, However, player two only stands to gain from being unkind if player one goes left. If player one goes right the rational player two would de facto be kind to her/him in that subgame. However, The non-credible threat of being unkind at 2(2) is still part of the blue (L, (U,U)) Nash equilibrium.
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The basic chemical equation of this process is: : Si(s) \+ 2 MgO(s) ↔ SiO2(s) \+ 2 Mg(g) (high temperature, distillation boiling zone) Silicon and magnesia react to produce silica and magnesium. Though, according to Ellingham diagrams, this reaction is thermodynamically unfavorable, in accordance with the Le Chatelier's principle of equilibria, it can still be driven to the right by continuous supply of heat, and by removing one of the products, namely distilling out the magnesium vapor. The atmospheric pressure boiling point of magnesium metal is very low, only 1090 °C, and even lower in vacuum. Vacuum is preferred, because it allows lower temperatures.
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But given this, Player 1 should choose D in the first round, receiving 1 instead of 0. There are a large number of Nash equilibria in a centipede game, but in each, the first player defects on the first round and the second player defects in the next round frequently enough to dissuade the first player from passing. Being in a Nash equilibrium does not require that strategies be rational at every point in the game as in the subgame perfect equilibrium. This means that strategies that are cooperative in the never-reached later rounds of the game could still be in a Nash equilibrium.
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If like preferred like, leucistic animals (such as white peacocks) would be sexually attracted to one another, and a leucistic subspecies would come into being. Koinophilia predicts that this is unlikely because leucistic animals are attracted to the average in the same way as are all the other members of its species. Since non-leucistic animals are not attracted by leucism, few leucistic individuals find mates, and leucistic lineages will rarely form. Koinophilia provides simple explanations for the almost universal canalization of sexual creatures into species, the rarity of transitional forms between species (between both extant and fossil species), evolutionary stasis, punctuated equilibria, and the evolution of cooperation.
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There are however several Nash equilibria. If both players choose the strategy (2, 2, 2) or (1, 2, 3), then none of them can beat the other one by changing strategies, so every such strategy pair is a Nash equilibrium. For larger S the game becomes progressively more difficult to analyze. For S = 12, it can be shown that (2, 4, 6) represents the optimal strategy, while for S > 12, deterministic strategies fail to be optimal. For S = 13, choosing (3, 5, 5), (3, 3, 7) and (1, 5, 7) with probability 1/3 each can be shown to be the optimal probabilistic strategy.
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His 1985 papers (with Jeremy Bulow and John Geanakoplos) developed the concept – and invented the terminology – of "strategic complements" that is now commonly used in game theory, industrial organisation and elsewhere.Multimarket Oligopoly, JPE His PhD thesis, and independent work by Carl Christian von Weizsacker, began the study of consumer switching costs.Switching Costs, QJE His paper on supply function equilibria (with Margaret Meyer) developed a standard model for the analysis of privatised electricity markets, and has been important in developing the theory of multiunit auctions.Supply Functions, Econometrica His papers (many of which are co-authored with Jeremy Bulow) apply ideas from auction theory to other economic contexts, including finance and political economy.
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Reviewing the history of macroevolutionary theories, the American evolutionary biologist Douglas J. Futuyma notes that since 1970, two very different alternatives to Darwinian gradualism have been proposed, both by Stephen Jay Gould: mutationism, and punctuated equilibria. Gould's macromutation theory gave a nod to his predecessor with an envisaged "Goldschmidt break" between evolution within a species and speciation. His advocacy of Goldschmidt was attacked with "highly unflattering comments" by Brian Charlesworth and Alan Templeton. Futuyma concludes, following other biologists reviewing the field such as K.Sterelny and A. Minelli,Minelli, A. (2010) "Evolutionary developmental biology does not offer a significant challenge to the neo-Darwinian paradigm".
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The Kakutani fixed-point theorem is a generalization of Brouwer's fixed- point theorem, holding for generalized correspondences instead of functions. Its most important uses are in proving the existence of Nash equilibria in game theory, and the Arrow–Debreu–McKenzie model of general equilibrium theory. Kakutani's other mathematical contributions include Markov–Kakutani fixed-point theorem, another fixed point theorem; the Kakutani skyscraper, a concept in ergodic theory (a branch of mathematics that studies dynamical systems with an invariant measure and related problems); his solution of the Poisson equation using the methods of stochastic analysis. The Collatz conjecture is also known as the Kakutani conjecture.
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The model and its competitive extensions have been used extensively in the literature.Bensoussan, A., Chen, S., Chutani, A., Sethi, S.P., Siu, C.C., and Yam, S.C.P., "Feedback Stackelberg- Nash Equilibria in Mixed Leadership Games with an Application to Cooperative Advertising," SIAM Journal on Control and Optimization, 2019, 57(5), 3413-3444. SSRN 3493916.Chutani A. and Sethi, S.P., "A Feedback Stackelberg Game of Cooperative Advertising in a Durable Goods Oligopoly," Dynamic Games in Economics, 13, J.L. Haunschmied, V. Veliov, and S. Wrzaczek (Eds.), Springer-Verlag Berlin Heidelberg, 2014, 89-114.Chutani, A. and Sethi, S.P., "Cooperative Advertising in a Dynamic Retail Market Oligopoly," Dynamic Games and Applications, 2(4), 2012, 347-375.
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He discovered the concept of chemical potential, or the "fuel" that makes chemical reactions work. In 1876 he published his most famous contribution, "On the Equilibrium of Heterogeneous Substances", a compilation of his work on thermodynamics and physical chemistry which laid out the concept of free energy to explain the physical basis of chemical equilibria. In these essays were the beginnings of Gibbs’ theories of phases of matter: he considered each state of matter a phase, and each substance a component. Gibbs took all of the variables involved in a chemical reaction - temperature, pressure, energy, volume, and entropy - and included them in one simple equation known as Gibbs' phase rule.
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The exposure of these economies to persistent shocks may lead to multiple equilibria outcomes: a country that under a tranquil condition may have a perfectly sustainable policy stance may suddenly jump to an unsustainable situation just because the fear of default leads international investors to ask for larger risk premium. In other words, if the market regards a country's state to be “good”, then large capital inflows can take place; if the market judges the country as being in a “bad” state, then rapid capital outflows and crisis can take place. In a “multiple” equilibrium environment, external shocks induce the economy to move from a “good” to a “bad” equilibrium.
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Jaynes theorized that a shift from bicameralism marked the beginning of introspection and consciousness as we know it today. According to Jaynes, this bicameral mentality began malfunctioning or "breaking down" during the 2nd millennium BCE. He speculates that primitive ancient societies tended to collapse periodically: for example, Egypt's Intermediate Periods, as well as the periodically vanishing cities of the Mayas, as changes in the environment strained the socio-cultural equilibria sustained by this bicameral mindset. The Bronze age collapse of the 2nd millennium BCE led to mass migrations and created a rash of unexpected situations and stresses which required ancient minds to become more flexible and creative.
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But its methodology, conceptual apparatus, and analytics "are derived, essentially, from the discipline that has as its subject the economic organization of such a society" (1962, p. v). The book focuses on positive-economic analysis as to the development of constitutional democracy but in an ethical context of consent. The consent takes the form of a compensation principle like Pareto efficiency for making a policy change and unanimity or at least no opposition as a point of departure for social choice. Somewhat later, the probabilistic voting theory started to displace the median voter theory in showing how to find Nash equilibria in multidimensional space.
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The application of these theories emerged in Kiyotaki and Wright (1993), when the authors developed a tractable model of the exchange process that captures the "double coincidence of wants problem" in a pure barter setup. In this model, the essential function of money is its role as a medium of exchange. The model can be used to address issues in monetary economics, such as the interaction between specialization and monetary exchange, and the possibility of equilibria with multiple fiat currencies. A shortcoming of search-theoretic models of money is that these models becomes intractable without very strong assumptions, and are therefore impractical for the analysis of monetary policy.
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Lavoisier and Berthollet, Chimistes Celebres, Liebig's Extract of Meat Company Trading Card, 1929 Claude Louis Berthollet statue in Annecy, France Claude Louis Berthollet (9 December 1748 in Talloires, France – 6 November 1822 in Arcueil, France) was a Savoyard-French chemist who became vice president of the French Senate in 1804. He is known for his scientific contributions to theory of chemical equilibria via the mechanism of reverse chemical reactions, and for his contribution to modern chemical nomenclature. On a practical basis, Berthollet was the first to demonstrate the bleaching action of chlorine gas, and was first to develop a solution of sodium hypochlorite as a modern bleaching agent.
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The material part of one tooth is slightly smaller than the space on the other and so shaped to act as a "contractible jaw"--the jaw is elastically opened and then closed as it goes over the other tooth. The "snug fit" that results when "one member nests within the recess of an adjoining member" is a stable locked state. The maximum force when the slider operates is in between the unlocked and locked positions, giving two stable mechanical equilibria. The "snug fit" is stable not only to forces from wear that act in the same direction as those of the slider but to transverse and longitudinal (both perpendicular) forces.
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Due to support from his mentor, J. M. van Bemmelen, he became an assistant at the University of Leiden in 1878, which enabled him to start his academic education there. In 1881 he became a teacher at a girls school, and in 1884 he obtained his PhD with works on the hydrates of acids. J. D. van der Waals introduced him to the theoretical works of J. Willard Gibbs on the phase rule which so far had little experimental verification in chemistry, prompting him to start a lifelong research programme on phase equilibria. In 1896, he became professor for chemistry in Amsterdam, where he died on February 8, 1907.
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The analysis differs in the continuous and discrete cases: in the former, methods from differential equations are utilized, whereas in the latter the methods tend to be stochastic. Since the replicator equation is non-linear, an exact solution is difficult to obtain (even in simple versions of the continuous form) so the equation is usually analyzed in terms of stability. The replicator equation (in its continuous and discrete forms) satisfies the folk theorem of evolutionary game theory which characterizes the stability of equilibria of the equation. The solution of the equation is often given by the set of evolutionarily stable states of the population.
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More complex models consider voter behavior when the voters reach a game-theoretical equilibrium from which they have no incentive, as defined by their internal preferences, to further change their behavior. However, because these equilibria are complex, only partial results are known. With respect to the voters' internal preferences, the two- round system passes the majority criterion in this model, as a majority can always coordinate to elect their preferred candidate. Also, in the case of three candidates or less and a robust political equilibrium, the two-round system will pick the Condorcet winner whenever there is one, which is not the case in the Contingent vote model.
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Elias Koutsoupias is a Greek computer scientist working in algorithmic game theory. Koutsoupias received his bachelor's degree in electrical engineering from the National Technical University of Athens and his doctorate in computer science in 1994 from the University of California, San Diego under the supervision of Christos Papadimitriou. He subsequently taught at the University of California, Los Angeles, the University of Athens, and is now a professor at the University of Oxford. In 2012, he was one of the recipients of the Gödel Prize for his contributions to algorithmic game theory, specifically the introduction of the price of anarchy concept with Papadimitriou in the paper 'Worst-case equilibria'.
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One of the most efficient and effective catalysts ever developed for the asymmetric hydrogenation of ketones, with a turnover number (TON) up to 4,550,000 and ee up to 99.9%, uses another iridium(I) system with a closely related tridentate ligand. alt=Two chemical diagrams Despite their similarities, the two functional groups are not identical; there are many areas where they diverge significantly. One of these is in the asymmetric hydrogenation of N-unfunctionalized imines to give primary amines. Such species can be difficult to selectively reduce because they tend to exist in complex equilibria of imine and enamine tautomers, as well as (E) and (Z) isomers.
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Binding, for instance to the carbonyl group of acetaldehyde, varies with the wine in question. The free form exists in equilibrium between molecular SO2 (as a dissolved gas) and bisulfite ion, which is in turn in equilibrium with sulfite ion. These equilibria depend on the pH of the wine. Lower pH shifts the equilibrium towards molecular (gaseous) SO2, which is the active form, while at higher pH more SO2 is found in the inactive sulfite and bisulfite forms. The molecular SO2 is active as an antimicrobial and antioxidant, and this is also the form which may be perceived as a pungent odor at high levels.
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The equilibrium mixed strategy for the minimizing player can be found by solving the dual of the given linear program. Or, it can be found by using the above procedure to solve a modified payoff matrix which is the transpose and negation of (adding a constant so it's positive), then solving the resulting game. If all the solutions to the linear program are found, they will constitute all the Nash equilibria for the game. Conversely, any linear program can be converted into a two-player, zero-sum game by using a change of variables that puts it in the form of the above equations.
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Like all chemical equilibria, these reactions behave according to Le Chatelier's principle, and the conditions that most favour carbamate formation have an unfavourable effect on the urea conversion equilibrium. The process conditions are, therefore, a compromise: the ill-effect on the first reaction of the high temperature (around 190 °C) needed for the second is compensated for by conducting the process under high pressure (140–175 bar), which favours the first reaction. Although it is necessary to compress gaseous carbon dioxide to this pressure, the ammonia is available from the ammonia plant in liquid form, which can be pumped into the system much more economically.
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In microeconomic theory, cost-minimization by consumers and by firms implies the existence of supply and demand correspondences for which market clearing equilibrium prices exist, if there are large numbers of consumers and producers. Under convexity assumptions or under some marginal-cost pricing rules, each equilibrium will be Pareto efficient: In large economies, non- convexity also leads to quasi-equilibria that are nearly efficient. However, the concept of market equilibrium has been criticized by Austrians, post- Keynesians and others, who object to applications of microeconomic theory to real-world markets, when such markets are not usefully approximated by microeconomic models. Heterodox economists assert that micro-economic models rarely capture reality.
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In these models the phase paths can "spiral in" towards zero, "spiral out" towards infinity, or reach neutrally stable situations called centres where the path traced out can be either circular, elliptical, or ovoid, or some variant thereof. This is useful in determining if the dynamics are stable or not. Other examples of oscillatory systems are certain chemical reactions with multiple steps, some of which involve dynamic equilibria rather than reactions that go to completion. In such cases one can model the rise and fall of reactant and product concentration (or mass, or amount of substance) with the correct differential equations and a good understanding of chemical kinetics.
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Although the model was simple, the assumption of limited participation extends to all dynamic models based on the overlapping generations model. Sunspot equilibria are important because they introduce the possibility that extraneous uncertainty may cause business cycles. The first paper to exploit this idea is due to Azariadis who introduced the term "self-fulfilling prophecy," a term he borrowed from Robert K. Merton, to refer to a complete dynamic model in which economic fluctuations arise simply because people believe that they will occur. The idea was extended by Roger Farmer and Michael Woodford to a class of autoregressive models and forms the basis for the Indeterminacy School in Macroeconomics.
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A synthetic quartz crystal grown by the hydrothermal method Hydrothermal synthesis includes the various techniques of crystallizing substances from high-temperature aqueous solutions at high vapor pressures; also termed "hydrothermal method". The term "hydrothermal" is of geologic origin.The earliest occurrence of the word "hydrothermal" appears to be: Sir Charles Lyell, A Manual of Elementary Geology … , 5th ed. (Boston, Massachusetts: Little, Brown, and Company, 1855), page 603: "The metamorphic theory [requires us to affirm] that an action, existing in the interior of the earth at an unknown depth, whether thermal, hydro-thermal, … " Geochemists and mineralogists have studied hydrothermal phase equilibria since the beginning of the twentieth century.
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Focusing his work on transport and reaction in nanostructured porous media, Bhatia has contributed to the field of catalysis, specifically in vapour-liquid and reaction equilibria in small pores. He elucidated multiphase reactions in catalyst particles by demonstrating the existence and consequence of partial internal wetting states. He was elected a fellow of the Institution of Chemical Engineers, Australia. He received the ExxonMobil Award for excellence of the Institution of Chemical Engineers in 2009, and the Institution of Chemical Engineers, UK (2008). He served on the ARC's Excellence in Research Australia Panel in 2012, and received the University of Queensland, Vice-Chancellor’s Research Excellence Award (2011).
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Democratizing innovation (2005) Eric von Hippel, MIT PressGeorg von Krogh (2008) "Researching the Private-Collective Innovation Model" The SAGE Handbook of New Approaches in Management and Organization, Daved Barry and Hans Hansen (ed.) Sage, 396-397. A laboratory studyGächter, S., von Krogh, G., Haefliger, S. "Initiating private-collective innovation: The fragility of knowledge sharing," Research Policy, 39(7), 2010, pp. 893-906. traced the initiation of private-collective innovation to the first decision to share knowledge in a two-person game with multiple equilibria. The results indicate fragility: when individuals face opportunity costs to sharing their knowledge with others they quickly turn away from the social optimum of mutual sharing.
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" Dutch Prime Minister Mark Rutte said Kohl was "a great statesman" who had shaped European history. Spanish Prime Minister Mariano Rajoy lauded Kohl's role in European history and in the German reunification. Polish Prime Minister Beata Szydło called Kohl "an outstanding figure and statesman, a great politician in exceptional times". Italian President Sergio Mattarella called Kohl one of Europe's founding fathers, and said that "he who was, rightly, described as 'the Chancellor of Reunification', worked with far-sightedness and determination, in years marked by deep and epochal changes in world equilibria, to give back unity to his country in the framework of the great project of European integration.
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Woodford's early research topics included sunspot equilibria, and imperfect competition. Thereafter he began to work on macroeconomic models with sticky prices; together with Julio Rotemberg he developed one of the first microfounded New Keynesian macroeconomic models. Since then he has used this framework to study many topics related to monetary policy, including the fiscal theory of the price level, the effectiveness of monetary policy as consumers use more credit and less cash, and inflation targeting rules. Michael Woodford has especially praised Knut Wicksell's advocacy of using the interest rate to maintain price stability, noting that this was a remarkable insight at a time when most monetary policy was based on the gold standard (Woodford, 2003, p. 32).
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But on Shackle's reading Keynes abandoned this "great undermining" of the "theory of value"—by which he meant any economics based on market equilibrium—in his General Theory instead falling back on a "curious methodology... where what is displayed to the reader is a range of 'equilibria' of the most precarious and ephemeral kind".G.L.S Shackle, "Epistemics & Economics: A Critique of Economic Doctrines" Cambridge University Press, p. 163. United Kingdom, 1972. Shackle writes that Keynes only really arrived at the true meaning of the revolution he had undertaken in Chapter 12 of the General Theory and then, more forcefully, in his 1937 article in the Quarterly Journal of Economics entitled The Theory of Employment.
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If either player changes their probabilities slightly, they will be both at a disadvantage, and their opponent will have no reason to change their strategy in turn. The (50%,50%) equilibrium is unstable. If either player changes their probabilities (which would neither benefit or damage the expectation of the player who did the change, if the other player's mixed strategy is still (50%,50%)), then the other player immediately has a better strategy at either (0%, 100%) or (100%, 0%). Stability is crucial in practical applications of Nash equilibria, since the mixed strategy of each player is not perfectly known, but has to be inferred from statistical distribution of their actions in the game.
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An equilibrium consists of a policy proposal by each party, such that no party can deviate to another policy that would increase the payoffs of all three of its factions. This concept, called Party Unanimity Nash Equilibrium (PUNE), can be viewed as involving Nash bargaining among factions within each party, and Nash equilibrium between parties. As well as capturing what appears to happen in party competition, PUNE has the virtue that it exists regardless of the dimension of the policy space. (In fact, with two parties, a two- dimensional set or manifold of equilibria generically exist, under reasonable conditions.) This theory was extended, and applied to a number of examples in Roemer (2001).
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A Chemical and Physical Foundations Thermodynamics and kinetics Redox states Water, pH, acid-base reactions and buffers Solutions and equilibria Solute-solvent interactions Chemical interactions and bonding Chemical reaction mechanisms B Structural Biology: Structure, Assembly, Organization and Dynamics Small molecules Macromolecules (e.g., nucleic acids, polysaccharides, proteins and complex lipids) Supramolecular complexes (e.g., membranes, ribosomes and multienzyme complexes) C Catalysis and Binding Enzyme reaction mechanisms and kinetics Ligand-protein interaction (e.g., hormone receptors, substrates and effectors, transport proteins and antigen-antibody interactions) D Major Metabolic Pathways Carbon, nitrogen and sulfur assimilation Anabolism Catabolism Synthesis and degradation of macromolecules E Bioenergetics (including respiration and photosynthesis) Energy transformations at the substrate level Electron transport Proton and chemical gradients Energy coupling (e.g.
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Although generally (assuming convexity) an equilibrium will exist and will be efficient, the conditions under which it will be unique are much stronger. The Sonnenschein–Mantel–Debreu theorem, proven in the 1970s, states that the aggregate excess demand function inherits only certain properties of individual's demand functions, and that these (Continuity, Homogeneity of degree zero, Walras' law and boundary behavior when prices are near zero) are the only real restriction one can expect from an aggregate excess demand function. Any such function can represent the excess demand of an economy populated with rational utility-maximizing individuals. There has been much research on conditions when the equilibrium will be unique, or which at least will limit the number of equilibria.
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Non-cooperative games are generally analysed through the framework of non-cooperative game theory, which tries to predict players' individual strategies and payoffs and to find Nash equilibria. It is opposed to cooperative game theory, which focuses on predicting which groups of players ("coalitions") will form, the joint actions that groups will take, and the resulting collective payoffs. Cooperative game theory does not analyze the strategic bargaining that occurs within each coalition and affects the distribution of the collective payoff between the members. Non-cooperative game theory provides a low-level approach as it models all the procedural details of the game, whereas cooperative game theory only describes the structure, strategies and payoffs of coalitions.
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However, playing Cournot would not have been the best response of the leader were it that the follower would play Stackelberg if it (the leader) played Stackelberg. In this case, the best response of the leader would be to play Stackelberg. Hence, what makes this profile (or rather, these profiles) a Nash equilibrium (or rather, Nash equilibria) is the fact that the follower would play non-Stackelberg if the leader were to play Stackelberg. However, this very fact (that the follower would play non-Stackelberg if the leader were to play Stackelberg) means that this profile is not a Nash equilibrium of the subgame starting when the leader has already played Stackelberg (a subgame off the equilibrium path).
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A Poet of Computation Who Uncovers Distant Truths Quanta Magazine He attended Varvakeio High School, and completed his undergraduate studies in the National Technical University of Athens, where in 2004 he received his Diploma in Electrical and Computer Engineering. He completed his undergraduate thesis "On the Existence of Pure Nash Equilibria in Graphical Games with succinct description" under the supervision of Stathis Zachos. As an undergraduate, Daskalakis attained perfect scores in all but one of his classes, something which had not previously been achieved in the university's history. He continued to study at University of California, Berkeley, where he received his PhD in Electrical Engineering and Computer Science in 2008 under the supervision of Christos Papadimitriou.
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In organic compounds, the weight percent of hydrocarbon chain often determines the compound's miscibility with water. For example, among the alcohols, ethanol has two carbon atoms and is miscible with water, whereas 1-butanol with four carbons is not. Octanol, with eight carbons, is practically insoluble in water, and its immiscibility leads it to be used as a standard for partition equilibria. The straight-chain carboxylic acids up to butanoic acid (with four carbon atoms) are miscible with water, pentanoic acid (with five carbons) is partly soluble, and hexanoic acid (with six) is practically insoluble, as are longer fatty acids and other lipids; the very long carbon chains of lipids cause them almost always to be immiscible with water.
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At finite temperature, the molecule spends most of its time in these low-lying states, which thus dominate the molecular properties. Global optimization can be accomplished using simulated annealing, the Metropolis algorithm and other Monte Carlo methods, or using different deterministic methods of discrete or continuous optimization. While the force field represents only the enthalpic component of free energy (and only this component is included during energy minimization), it is possible to include the entropic component through the use of additional methods, such as normal mode analysis. Molecular mechanics potential energy functions have been used to calculate binding constants, protein folding kinetics, protonation equilibria, active site coordinates, and to design binding sites.
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After his return to Germany in 1891, he obtained the highest academic degree, the Habilitation, working under the direction of Adolf von Baeyer in Munich on the determination of the equilibrium of the Keto-enol tautomerism of ethyl acetoacetate. This was done through the determination of the Enol content in Keto-Enol-tautomerism equilibria via titration of bromine (“Ueber die Keto-Enol Tautomerie”). The Meyer-Schuster rearrangement and the "Meyer’s Back Titration" method bear his name. In World War I, beginning in 1914, Meyer served as an officer in the artillery, however he was called in 1917 to carry out warfare research work in the Kaiser Wilhelm Society Institute in Berlin under the direction of Fritz Haber.
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In real-world markets, assumptions such as perfect information cannot be verified and are only approximated in organized double-auction markets where most agents wait and observe the behaviour of prices before deciding to exchange (but in the long-period interpretation perfect information is not necessary, the analysis only aims at determining the average around which market prices gravitate, and for gravitation to operate one does not need perfect information). In the absence of externalities and public goods, perfectly competitive equilibria are Pareto-efficient, i.e. no improvement in the utility of a consumer is possible without a worsening of the utility of some other consumer. This is called the First Theorem of Welfare Economics.
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In game theory a strong Nash equilibrium is a Nash equilibrium in which no coalition, taking the actions of its complements as given, can cooperatively deviate in a way that benefits all of its members. While the Nash concept of stability defines equilibrium only in terms of unilateral deviations, strong Nash equilibrium allows for deviations by every conceivable coalition. This equilibrium concept is particularly useful in areas such as the study of voting systems, in which there are typically many more players than possible outcomes, and so plain Nash equilibria are far too abundant. The strong Nash concept is criticized as too "strong" in that the environment allows for unlimited private communication.
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A variant for three players was introduced in 2010 by Nick Abou Risk and Duane Szafron. In this version, the deck includes four cards (adding a ten card), from which three are dealt to the players; otherwise, the basic structure is the same: while there is no outstanding bet, a player can check or bet, with an outstanding bet, a player can call or fold. If all players checked or at least one player called, the game proceeds to showdown, otherwise, the betting player wins. A family of Nash equilibria for 3-player Kuhn poker is known analytically, which makes it the largest game with more than two players with analytic solution.
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Suppose also that S is a best response to B. Hence, {S,B} is a Nash equilibrium. Let there be another Nash equilibrium {S',B'}, the outcome of which player 1 prefers and B' is the only best response to S'. In a dynamic game, the first Nash equilibrium is implausible (if player 1 moves first) because player 1 will play S', forcing the response (say) B' from player 2 and thereby attaining the second equilibrium (regardless of the preferences of player 2 over the equilibria). The first equilibrium is subgame imperfect because B does not constitute a best response to S' once S' has been played, i.e. in the subgame reached by player 1 playing S', B is not optimal for player 2.
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There are several implications one can derive from this model: # Workers performing the same task earn higher wages in a high-skill firm than in a low-skill firm; # Wages will be more than proportionately higher in developed countries than would be assumed by measurements of skill levels; # Workers will consider human capital investments in light of similar investments by those around them; # This model magnifies the effect of local bottlenecks which also reduce the expected returns to skill; # O-ring effects across firms can create national low- production traps. This model helps explain brain drain and international economic disparity. As Kremer puts it, "If strategic complementarity is sufficiently strong, microeconomically identical nations or groups within nations could settle into equilibria with different levels of human capital".
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In 1980, he was director of the Ministry of Defense, in 1982 the Ministry of Public Health, and from 1984 to 1986 the Ministry for the Economy. In July 1986, before the deterioration of the financial situation in the country, President Bourguiba discharged his Prime Minister Mohamed Mzali and tasked Rachid Sfar with implementing a structural adjustment plan as Prime Minister. Rachid Sfar re-established Tunisia's macro- economic equilibria by passing in the National Assembly the "Loi de finances complémentaire" (the supplemental finances law), by devaluing the dinar by 10%, and by obtaining support from the International Monetary Fund and the World Bank to rebuild currency reserves and re-establish credit. President Habib Bourguiba fired Rachid Sfar on 3 October 1987.
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Because stellarators are non-axisymmetric, the CTH group uses the V3FIT and VMEC codes for reconstructing equilibria. The V3FIT code uses as inputs the currents in the magnetic confinement coils, the plasma current, and data from the various diagnostics such as the Rogowski coils, SXR cameras, and interferometer. The output of the V3FIT code includes the structure of the magnetic field, and profiles of the plasma current, density, and SXR emissivity. Data from the CTH experiment was and continues to be used as a testbed for the V3FIT code which has also used for equilibrium reconstruction on the Helically Symmetric eXperiment (HSX), Large Helical Device (LHD), and Wendelstein 7-X (W7-X) stellarators, and the Reversed-Field eXperiment (RFX) and Madison Symmetric Torus (MST) reversed field pinches.
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Scale build-up effectively decreases pipeline diameter and reduces flow rate The three prevailing water-related problems that upset oil companies today are corrosion, gas hydrates and scaling in production systems. The reservoir water has a high composition of dissolved minerals equilibrated over millions of years at constant physicochemical conditions. As the reservoir fluids are pumped from the ground, changes in temperature, pressure and chemical composition shift the equilibria and cause precipitation and deposition of sparingly soluble salts that build up over time with the potential of blocking vital assets in the oil production setups. Scaling can occur at all stages of oil/gas production systems (upstream, midstream and downstream) and causes blockages of well-bore perforations, casing, pipelines, pumps, valves etc.
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In this case, the zoo would purchase either one lion or one eagle. Of course, a contemporary zoo-keeper does not want to purchase a half an eagle and a (or a griffin)! Thus, the contemporary zoo-keeper's preferences are non‑convex: The zoo-keeper prefers having either animal to having any strictly convex combination of both. Non‑convex sets have been incorporated in the theories of general economic equilibria,Pages 392–399 and page 188: Pages 52–55 with applications on pages 145–146, 152–153, and 274–275: Theorem C(6) on page 37 and applications on pages 115–116, 122, and 168: of market failures,Pages 112–113 in Section 7.2 "Convexification by numbers" (and more generally pp.
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In acid base physiology, the Davenport diagram is a graphical tool, developed by Horace W. Davenport, that allows a clinician or investigator to describe blood bicarbonate concentrations and blood pH following a respiratory and/or metabolic acid-base disturbance. The diagram depicts a three-dimensional surface describing all possible states of chemical equilibria between gaseous carbon dioxide, aqueous bicarbonate and aqueous protons at the physiologically complex interface of the alveoli of the lungs and the alveolar capillaries. Although the surface represented in the diagram is experimentally determined, the Davenport diagram is primarily a conceptual tool, allowing the investigator to envision the effects of physiological changes on blood acid- base chemistry. The Davenport diagram is rarely used in the clinical setting.
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This is inconsistent with the quantities of capital goods being taken as data. But when Walras introduced capital goods in his later models, he took their quantities as given, in arbitrary ratios. (In contrast, Kenneth Arrow and Gérard Debreu continued to take the initial quantities of capital goods as given, but adopted a short run model in which the prices of capital goods vary with time and the own rate of interest varies across capital goods.) Walras was the first to lay down a research program much followed by 20th-century economists. In particular, the Walrasian agenda included the investigation of when equilibria are unique and stable— Walras' Lesson 7 shows neither uniqueness, nor stability, nor even existence of an equilibrium is guaranteed.
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Several of his essays on this topic are included in Islam and Mammon: The Economic Predicaments of Islamism (Princeton University Press), which has been translated into Turkish and Arabic. Since the mid-1990s he has turned his attention to the conundrum of why the Middle East, which once had a high standard of living by global standards, subsequently fell behind in various realms, including economic production, organizational capability, technological creativity, democratization, and military strength. His thesis is that the economic and educational institutions of Islam, though well-suited to the era in which they emerged, were poorly suited to a dynamic industrial economy. These institutions fostered social equilibria that reduced the likelihood of modern capitalism emerging from within Islamic civilization.
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When this happens, economic agents outside of the industry find no advantage to forming new firms that enter into the industry, the supply of the product stops increasing, and the price charged for the product stabilizes, settling into an equilibrium. The same is likewise true of the long run equilibria of monopolistically competitive industries and, more generally, any market which is held to be contestable. Normally, a firm that introduces a differentiated product can initially secure a temporary market power for a short while (See "Persistence" in Monopoly Profit). At this stage, the initial price the consumer must pay for the product is high, and the demand for, as well as the availability of the product in the market, will be limited.
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Pagano has shown that while public goods are typically undersupplied, positional goods are typically oversupplied. For what concerns instead intelligence scarcity he has suggested that bounded rationality has many dimensions each of which can be represented as a maximisation problem with some additional constraints, only at the cost of contradicting the scarcity assumption at a higher level. In the literature on the theory of the firm the main contribution of Pagano has been the development of the concept of organizational equilibrium. Combining the literatures of the Neo- institutional and Radical schools he has defined organizational equilibria as situations where a set of rights (technological characteristics of the resources) brings about technological characteristics of the resources (rights) which are consistent with this set of rights (technology).
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This work was followed very quickly by results showing that the non-existence problem pointed out by Hart was not generic, and led ultimately to the generic existence results of Duffie and Shafer, and again spawned a new literature looking positively at the welfare implication of market incompleteness, and normatively at issues of asset engineering. In the time after this seminal work in GEI, Cass's various papers dealt with issues of determinacy of equilibrium (and the closely related issue of existence of sunspot equilibria), and with the optimality of allocations in the presence of sunspots and incomplete asset markets. These papers include: :• "The structure of financial equilibrium with exogenous yields: The case of incomplete markets" (with Y. Balasko). Econometrica 57, 135-162 (1989).
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An acidic solution, on the other hand, is very hazardous because all the cyanide is in its acid form. Ingestion of cyanide by mouth is potentially fatal, independently of pH, because of the reaction with cytochrome c oxidase. In environmental science acid–base equilibria are important for lakes Chapter 9-6: Acid Rain and the Buffer Capacity of Lakes and rivers; for example, humic acids are important components of natural waters. Another example occurs in chemical oceanography: in order to quantify the solubility of iron(III) in seawater at various salinities, the pKa values for the formation of the iron(III) hydrolysis products Fe(OH)2+, and Fe(OH)3 were determined, along with the solubility product of iron hydroxide.
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This started a shift in macroeconomics away from using the model of perfect competition with price taking agents to using imperfectly competitive equilibria with price and wage setting agents (mostly adopting monopolistic competition). Huw Dixon and Claus Hansen showed that even if menu costs applied to a small sector of the economy, this would influence the rest of the economy and lead to prices in the rest of the economy becoming less responsive to changes in demand. In 2007, Mikhail Golosov and Robert Lucas found that the size of the menu cost needed to match the micro-data of price adjustment inside an otherwise standard business cycle model is implausibly large to justify the menu-cost argument. The reason is that such models lack "real rigidity".
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Crompton outspokenly rejected Fabre's arguments that the behaviour of such creatures as hunting-wasps, that operated by injecting venom precisely into particular nerve-centres, could not have arisen by natural selection. Fabre's views of Darwinism made little impression at the height of Darwin's fame. In the twentieth Century, various refinements to Classical Darwinism, such as the theory of Punctuated Equilibria, and deeper understanding of the principles and practicalities of molecular biology, made serious progress in addressing problems of the mechanism of evolution of complex structures and behaviour patterns. This includes dealing with many difficulties where it seems impossible for an attribute to have arisen in a half-formed state: until they are perfected, such attributes ought, by the hypothesis itself, to have been eliminated through natural selection.
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When a roly-poly toy is pushed, the height of the center of mass rises from the green line to the orange line, and the center of mass is no longer over the point of contact with the ground. In geometry, a body with a single stable resting position is called monostatic, and the term mono- monostatic has been coined to describe a body which additionally has only one unstable point of balance. (The previously known monostatic polyhedron does not qualify, as it has three unstable equilibria.) A sphere weighted so that its center of mass is shifted from the geometrical center is a mono-monostatic body. A more common example is the Comeback Kid, Weeble or roly-poly toy (see left figure).
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Research Interests - Electrochemistry Mechanisms of some organic reactions are investigated using polarographic, voltammetric and kinetic measurements. Examples of recently studied reactions are: Acid-base, hydration-dehydration and tautomeric equilibria involving 1,3,5- and 1,2,4-triazines, selenous acid and mytomicin C, reactions of bile acids, cholesterol, and other sterols in strongly acidic media, additions of nucleophiles, such as glutathione, to nitrosobenzene, etc. Most of these studies involve biologically important compounds and their investigations are essential both for development of analytical methods and for their contribution to a better understanding of biological activity. Another active area are studies of electroreduction and electrooxidation of some organic compounds, such as aromatic nitrocompounds, various pesticides including maleic hydrazide, 1,3,5- and 1,2,4-triazines, selenous acid, mitomycin C, phenols, etc.
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For local attractors, a conjecture on the Lyapunov dimension of self-excited attractor, refined by N. Kuznetsov, is stated that for a typical system, the Lyapunov dimension of a self-excited attractor does not exceed the Lyapunov dimension of one of the unstable equilibria, the unstable manifold of which intersects with the basin of attraction and visualizes the attractor. The conjecture is valid, e.g., for the classical self-excited Lorenz attractor; for the self-excited attractors in the Henon map (even in the case of multistability and coexistence of local attractors with different Lyapunov dimensions). For a hidden attractor the conjecture is that the maximum of the local Lyapunov dimensions is achieved on an unstable periodic orbit embedded into the attractor.
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Le Chatelier's principle (pronounced or ), also called Chatelier's principle or "The Equilibrium Law", is a principle of chemistry used to predict the effect of a change in conditions on chemical equilibria. The principle is named after French chemist Henry Louis Le Chatelier, and sometimes also credited to Karl Ferdinand Braun, who discovered it independently. It can be stated as: It is common to treat the principle as a more general observation of systems, such as or, "roughly stated", The concept of systemic maintenance of an equilibrium state despite perturbations has a variety of names, depending upon the discipline using it (e.g. homeostasis, an idea which encompasses the concept, is commonly used in biology), and has been studied in a variety of contexts, chiefly in the natural sciences.
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The game given in Figure 2 is a coordination game if the following payoff inequalities hold for player 1 (rows): A > B, D > C, and for player 2 (columns): a > b, d > c. The strategy pairs (H, H) and (G, G) are then the only pure Nash equilibria. In addition there is a mixed Nash equilibrium where player 1 plays H with probability p = (d-c)/(a-b-c+d) and G with probability 1–p; player 2 plays H with probability q = (D-C)/(A-B-C+D) and G with probability 1–q. Strategy pair (H, H) payoff dominates (G, G) if A ≥ D, a ≥ d, and at least one of the two is a strict inequality: A > D or a > d.
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The numerous cavities and crevices and the richness and diversity of the available food spectrum favour the development of juvenile forms of numerous species, reducing mortality.Casellato S., Masiero L., Sichirollo E., Soresi S., Hidden secrets of the Northern Adriatic: “Tegnùe”, peculiar reefs, Central European Journal of Biology 2 (1), 2007: 122-136. The equilibrium within such complex biocoenosis is determined by interactions between environmental and biological factors whose variations can modify the equilibria which define it. The tegnue seem to also create a marked diversification of populations within themselves due to the abundance of microenvironments and ridges and their distribution from the low-depth coastal areas more directly influenced by continental fluvial inputs to more offshore ones under greater water pressure in a high sedimentation and low brightness regime.
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As a result, the grain size decreases with increasing TaC addition which improves the yield stress explained by Hall- Petch relationship. The formation of lamellar structure is because at elevated temperature, the decomposition reaction occurs in the MoNbRe0.5W(TaC)x composites: (Mo, Nb, W, Ta)2C → (Mo, Nb, W, Ta) + (Mo, Nb, W, Ta)C in which Re is dissolved in both components to nucleate BCC phase first and MC phase in the following, according to the phase diagrams E. Rudy, S. Windisch, C.E. Brukl, Technical Report No. AFML-TR-65-2, Part II, Ternary Phase Equilibria in Transition Metal Boron-carbon-silicon Systems, vol. XVII, 1967. In addition, the MC phase also improves the strength of composites, due to its stiffer and more elastic property compared to BCC phase Wei, Qinqin, et al.
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At the Lagrange points the gravitational forces of the two large bodies cancel out in such a way that a small object placed in orbit there is in equilibrium relative to the center of mass of the large bodies. There are five such points, labeled L1 to L5, all in the orbital plane of the two large bodies. L1, L2, and L3 are on the line through the centers of the two large bodies, while L4 and L5 each act as the third vertex of an equilateral triangle formed with the centers of the two large bodies. L1, L2, L3 are unstable equilibria, whereas L4 and L5 are stable, which implies that objects can orbit around them in a rotating coordinate system tied to the two large bodies.
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107–115): and of public economics.Pages 63–65: These results are described in graduate-level textbooks in microeconomics, Page 628: general equilibrium theory,Page 169 in the first edition: In Ellickson, page xviii, and especially Chapter 7 "Walras meets Nash" (especially section 7.4 "Nonconvexity" pages 306–310 and 312, and also 328–329) and Chapter 8 "What is Competition?" (pages 347 and 352): game theory,Theorem 1.6.5 on pages 24–25: mathematical economics,Pages 127 and 33–34: and applied mathematics (for economists).Pages 93–94 (especially example 1.92), 143, 318–319, 375–377, and 416: Page 309: Pages 47–48: The Shapley–Folkman lemma results establish that non‑convexities are compatible with approximate equilibria in markets with many consumers; these results also apply to production economies with many small firms.
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An economic bubble or asset bubble (sometimes also referred to as a speculative bubble, a market bubble, a price bubble, a financial bubble, a speculative mania, or a balloon) is a situation in which asset prices appear to be based on implausible or inconsistent views about the future. It could also be described as trade in an asset at a price or price range that strongly exceeds the asset's intrinsic value. While some economists deny that bubbles occur, the causes of bubbles remain disputed by those who are convinced that asset prices often deviate strongly from intrinsic values. Many explanations have been suggested, and research has recently shown that bubbles may appear even without uncertainty, speculation, or bounded rationality, in which case they can be called non-speculative bubbles or sunspot equilibria.
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Brewer's dual appointment afforded him the opportunity to take an active role in all levels of academic instruction, both inside and outside of the laboratory. Besides providing classroom instruction in solid-state chemistry, heterogeneous equilibria, and inorganic chemistry, Brewer also delivered lectures and supervised laboratory work for laboratory courses in freshman chemistry, advanced quantitative analysis, instrumental analysis, inorganic synthesis, inorganic reactions, and organic chemistry, as well as courses in chemical thermodynamics from the sophomore to graduate student level. In order to ensure a high standard of instruction at even the most basic levels, Brewer initiated a course for freshman-chemistry teaching assistants that reviewed principles and certified their ability to adequately fulfill their responsibilities. Brewer was a caring and gifted teacher who was greatly admired by students and colleagues alike.
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Pinpointing the extinction (or pseudoextinction) of a species requires a clear definition of that species. If it is to be declared extinct, the species in question must be uniquely distinguishable from any ancestor or daughter species, and from any other closely related species. Extinction of a species (or replacement by a daughter species) plays a key role in the punctuated equilibrium hypothesis of Stephen Jay Gould and Niles Eldredge.See: Niles Eldredge, Time Frames: Rethinking of Darwinian Evolution and the Theory of Punctuated Equilibria, 1986, Heinemann Skeleton of various extinct dinosaurs; some other dinosaur lineages still flourish in the form of birds In ecology, extinction is often used informally to refer to local extinction, in which a species ceases to exist in the chosen area of study, but may still exist elsewhere.
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As the economy diversifies and exposes to a global environment by opening up to foreign direct investments and increasing foreign ownership of land and capital, cultural, religious and national identity equilibria are upset and jeopardize social security and political stability. Many have argued that political power in UAE's constitutional monarchies relies upon a 'ruling bargain' with the local population, that is, a delicate balance of elements of legitimacy strictly dependent on local culture and religion, as well as on how the wealth is redistributed within the country.Davidson, Christopher M., “The United Arab Emirates: a Study in Survival”, Boulder (2005). To the extent that economic diversification, globalization and urbanization do upset this balance, rulers have an interest in investing in the preservation of what is deemed to be an important source of their power.
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Until the 1990s, simple adaptive models, such as Cournot competition or fictitious play, were generally used. In the mid-1990s, Alvin E. Roth and Ido Erev demonstrated that reinforcement learning can make useful predictions in experimental games.Predicting how people play games: Reinforcement learning in experimental games with unique, mixed strategy equilibria,Ido Erev, Alvin E Roth,American economic review,1998/9/1,848-881 In 1999, Colin Camerer and Teck-Hua Ho introduced Experience Weighted Attraction (EWA), a general model that incorporated reinforcement and belief learning, and shows that fictitious play is mathematically equivalent to generalized reinforcement, provided weights are placed on past history. Criticisms of EWA include overfitting due to many parameters, lack of generality over games, and the possibility that the interpretation of EWA parameters may be difficult.
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In Power in Movement: Social Movements and Contentious Politics, Tarrow suggests that the conditions of a political and social environment influence the likelihood of and possibilities for contentious collective action, as "changes in political opportunities and constraints create the most important incentives for initiating new phases of contention." Steven Livingston follows a similar line of theory introduced by Bryan D. Jones and Frank R. Baumgartner in discussing the conditions of political change, arguing that "bursts of rapid and often unpredictable policy change punctuate the patterns of relatively long-term policy equilibria." In "Networks of Outrage and Hope" Manuel Castells argues that movements are “usually triggered by a spark of indignation related to a specific event or to a peak of disgust with the actions of the rulers.” (2012, p. 224).
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Hargreaves-Heap and Varoufakis found that the players' behavior within a session frequently developed a discriminatory convention, giving a Nash equilibrium where players of one color (the "advantaged" color) consistently played the aggressive "hawk" strategy against players of the other, "disadvantaged" color, who played the acquiescent "dove" strategy against the advantaged color. Players of both colors used a mixed strategy when playing against players assigned the same color as their own. The experimenters then added a cooperation option to the game, and found that disadvantaged players usually cooperated with each other, while advantaged players usually did not. They state that while the equilibria reached in the original hawk-dove game are predicted by evolutionary game theory, game theory does not explain the emergence of cooperation in the disadvantaged group.
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The Benesi–Hildebrand method is a mathematical approach used in physical chemistry for the determination of the equilibrium constant K and stoichiometry of non-bonding interactions. This method has been typically applied to reaction equilibria that form one-to-one complexes, such as charge- transfer complexes and host–guest molecular complexation. :{H} + G <=> HG The theoretical foundation of this method is the assumption that when either one of the reactants is present in excess amounts over the other reactant, the characteristic electronic absorption spectra of the other reactant are transparent in the collective absorption/emission range of the reaction system. Therefore, by measuring the absorption spectra of the reaction before and after the formation of the product and its equilibrium, the association constant of the reaction can be determined.
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In economics, the Edgeworth conjecture is the idea, named after Francis Ysidro Edgeworth, that the core of an economy shrinks to the set of Walrasian equilibria as the number of agents increases to infinity. The core of an economy is a concept from cooperative game theory defined as the set of feasible allocations in an economy that cannot be improved upon by subset of the set of the economy's consumers (a coalition). For general equilibrium economies typically the core is non-empty (there is at least one feasible allocation) but also "large" in the sense that there may be a continuum of feasible allocations that satisfy the requirements. The conjecture basically states that if the number of agents is also "large" then the only allocations in the core are precisely what a competitive market would produce.
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44: 365-378. They found that, as hypothesized by Nash, mixed strategy equilibria emerge when the subject values of options being mixed are equivalent. Glimcher's laboratory has conducted extensive research on the brain's reward system, in particular the dopamine system and reinforcement learning. In 2005, with Hannah Bayer, he published the first quantitative test of the Dopamine Reward Prediction Error Hypothesis based on single neuron recordings from dopamine neurons and a novel kernel- based analysis in Neuron.Bayer, H.M. and Glimcher, P.W. (2005) Midbrain Dopamine Neurons Encode a Quantitative Reward Prediction Error Signal. Neuron. 47: 129-141. In 2007 Glimcher and Joe Kable were the first to demonstrate a clear subject value signal in the human brain that could be effectively disassociated from objective value signals. This finding was published in Nature Neuroscience.Kable, J.W., and Glimcher, P.W. (2007).
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Cooperative games are often analyzed through the framework of cooperative game theory, which focuses on predicting which coalitions will form, the joint actions that groups take, and the resulting collective payoffs. It is opposed to the traditional non- cooperative game theory which focuses on predicting individual players' actions and payoffs and analyzing Nash equilibria. Cooperative game theory provides a high-level approach as it describes only the structure, strategies, and payoffs of coalitions, whereas non-cooperative game theory also looks at how bargaining procedures will affect the distribution of payoffs within each coalition. As non-cooperative game theory is more general, cooperative games can be analyzed through the approach of non-cooperative game theory (the converse does not hold) provided that sufficient assumptions are made to encompass all the possible strategies available to players due to the possibility of external enforcement of cooperation.
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This can be done by chemical-shift mapping, which is seeing which resonances are shifted upon binding of the other molecule, or by cross- saturation experiments where one of the binding molecules is selectively saturated and, if bound, the saturation transfers to the other molecule in the complex. Dynamic properties such as duplex–single strand equilibria and binding rates of other molecules to duplexes can also be determined by its effect on the spin–lattice relaxation time T1, but these methods are insensitive to intermediate rates of 104–108 s−1, which must be investigated with other methods such as solid-state NMR. Dynamics of mechanical properties of a nucleic acid double helix such as bending and twisting can also be studied using NMR. Pulsed field gradient NMR experiments can be used to measure diffusion constants.
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The same is likewise true of the long run equilibria of monopolistically competitive industries and, more generally, any market which is held to be contestable. Normally, a firm that introduces a differentiated product can initially secure a temporary market power for a short while (See Monopoly Profit § Persistence). At this stage, the initial price the consumer must pay for the product is high, and the demand for, as well as the availability of the product in the market, will be limited. In the long run, however, when the profitability of the product is well established, and because there are few barriers to entry, the number of firms that produce this product will increase until the available supply of the product eventually becomes relatively large, the price of the product shrinks down to the level of the average cost of producing the product.
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He was Executive Managing Director of Max-Planck-Institute for Metals Research in Stuttgart and also Professor at the Universities of Stuttgart and Berlin, where he taught courses in equilibrium phase diagrams and powder metallurgy; he is now retired. His main scientific interests dealt with problems in the field of physical metallurgy, powder metallurgy, special ceramics and phase diagrams of metallic and ceramic materials. He is the author and co-author of more than 600 research papers, 10 books, and holds 27 patents. Some of his most important papers and publications are on phase equilibria between intermetallic compounds to the knowledge of peritectic reactions, constitution and properties of cermets, metallography, high-temperature materials, Beryllium and its compounds, liquid phase sintering, particle rearrangement, metallographic etching, toughening of ceramics, Sialon ceramics, sintering of Si3N4 ceramics, metal-ceramic interfaces and processing of advanced ceramics.
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When an isosbestic plot is constructed by the superposition of the absorption spectra of two species (whether by using molar absorptivity for the representation, or by using absorbance and keeping the same molar concentration for both species), the isosbestic point corresponds to a wavelength at which these spectra cross each other. A pair of substances can have several isosbestic points in their spectra. When a 1-to-1 (one mole of reactant gives one mole of product) chemical reaction (including equilibria) involves a pair of substances with an isosbestic point, the absorbance of the reaction mixture at this wavelength remains invariant, regardless of the extent of reaction (or the position of the chemical equilibrium). This occurs because the two substances absorb light of that specific wavelength to the same extent, and the analytical concentration remains constant.
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The second crucial factor is the availability of computer software for calculating equilibria and various kinds of diagrams and databases with the stored assessed information. As there are at present many different kinds of models used for different kinds of phases there are several thermodynamic databases available, either free or commercially, for different materials like steels, super-alloys, semiconductor materials, aqueous solutions, slags, etc. There are also several different kinds of software available using different kinds of algorithms for computing the equilibrium. It is an advantage if the software allows the equilibrium to be calculated using many different types of conditions for the system, not only the temperature, pressure and overall composition because in many cases the equilibrium may be determined at constant volume or at a given chemical potential of an element or a given composition of a particular phase.
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Local thermodynamic equilibrium of matter (see also Keizer (1987) means that conceptually, for study and analysis, the system can be spatially and temporally divided into 'cells' or 'micro-phases' of small (infinitesimal) size, in which classical thermodynamical equilibrium conditions for matter are fulfilled to good approximation. These conditions are unfulfilled, for example, in very rarefied gases, in which molecular collisions are infrequent; and in the boundary layers of a star, where radiation is passing energy to space; and for interacting fermions at very low temperature, where dissipative processes become ineffective. When these 'cells' are defined, one admits that matter and energy may pass freely between contiguous 'cells', slowly enough to leave the 'cells' in their respective individual local thermodynamic equilibria with respect to intensive variables. One can think here of two 'relaxation times' separated by order of magnitude.
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It is > usually asserted that only aggregate neoclassical theory of the textbook > variety -- and hence macroeconomic theory, based on aggregate production > functions -- is affected by capital reversing. It has been pointed out, > however, that when neoclassical general equilibrium models are extended to > long-run equilibria, stability proofs require the exclusion of capital > reversing (Schefold 1997). In that sense, all neoclassical production models > would be affected by capital reversing." (Lavoie 2000) > "These findings destroy, for example, the general validity of Heckscher- > Ohlin-Samuelson international trade theory (as authors such as Sergio > Parrinello, Stanley Metcalfe, Ian Steedman, and Lynn Mainwaring have > demonstrated), of the Hicksian neutrality of technical progress concept (as > Steedman has shown), of neoclassical tax incidence theory (as Steedman and > Metcalfe have shown), and of the Pigouvian taxation theory applied in > environmental economics (as Gehrke and Lager have shown).
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Cooperative games are often analysed through the framework of cooperative game theory, which focuses on predicting which coalitions will form, the joint actions that groups take and the resulting collective payoffs. It is opposed to the traditional non-cooperative game theory which focuses on predicting individual players' actions and payoffs and analyzing Nash equilibria. Cooperative game theory provides a high-level approach as it only describes the structure, strategies and payoffs of coalitions, whereas non-cooperative game theory also looks at how bargaining procedures will affect the distribution of payoffs within each coalition. As non-cooperative game theory is more general, cooperative games can be analyzed through the approach of non-cooperative game theory (the converse does not hold) provided that sufficient assumptions are made to encompass all the possible strategies available to players due to the possibility of external enforcement of cooperation.
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For example, hyaluronan helps partition plasma proteins between vascular and extravascular spaces, which affects solubility of macromolecules in the interstitium, changes chemical equilibria, and stabilizes the structure of collagen fibers. :Other functions include matrix interactions with hyaluronan binding proteins such as hyaluronectin, glial hyaluronan binding protein, brain enriched hyaluronan binding protein, collagen VI, TSG-6, and inter-alpha-trypsin inhibitor. Cell surface interactions involving hyaluronan are its well-known coupling with CD44, which may be related to tumor progression, and also with RHAMM (Hyaluronan-mediated motility receptor), which has been implicated in developmental processes, tumor metastasis, and pathological reparative processes. Fibroblasts, mesothelial cells, and certain types of stem cells surround themselves in a pericellular "coat", part of which is constructed from hyaluronan, in order to shield themselves from bacteria, red blood cells, or other matrix molecules.
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More ammonia would be produced if the reaction were run at a lower temperature, but a lower temperature also lowers the rate of the process, so, in practice (the Haber process) the temperature is set at a compromise value that allows ammonia to be made at a reasonable rate with an equilibrium concentration that is not too unfavorable. In exothermic reactions, an increase in temperature decreases the equilibrium constant, K, whereas in endothermic reactions, an increase in temperature increases K. Le Chatelier's principle applied to changes in concentration or pressure can be understood by giving K a constant value. The effect of temperature on equilibria, however, involves a change in the equilibrium constant. The dependence of K on temperature is determined by the sign of ΔH. The theoretical basis of this dependence is given by the Van 't Hoff equation.
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Nash proved that if we allow mixed strategies (where a player chooses probabilities of using various pure strategies), then every game with a finite number of players in which each player can choose from finitely many pure strategies has at least one Nash equilibrium (which might be a pure strategy for each player or might be a probability distribution over strategies for each player). Nash equilibria need not exist if the set of choices is infinite and noncompact. An example is a game where two players simultaneously name a number and the player naming the larger number wins. Another example is where each of two players chooses a real number strictly less than 5 and the winner is whoever has the biggest number; no biggest number strictly less than 5 exists (if the number could equal 5, the Nash equilibrium would have both players choosing 5 and tying the game).
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Diffusion is a fundamental physical phenomenon, which Albert Einstein characterized as Brownian motion, that describes the random thermal movement of molecules and small particles in gases and liquids. It is an important phenomenon for small distances (it is essential for the achievement of thermodynamic equilibria), but, as the time necessary to cover a distance by diffusion is proportional to the square of the distance itself, it is ineffective for spreading a solute over macroscopic distances. The diffusion coefficient, D, is typically quite small, and its effect can often be considered negligible (unless groundwater flow velocities are extremely low, as they are in clay aquitards). It is important not to confuse diffusion with dispersion, as the former is a physical phenomenon and the latter is an empirical factor which is cast into a similar form as diffusion, because we already know how to solve that problem.
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In a synthesis report published in Science in 2015, 22 leading marine scientists stated that from burning fossil fuels is changing the oceans' chemistry more rapidly than at any time since the Great Dying, Earth's most severe known extinction event, emphasizing that the 2 °C maximum temperature increase agreed upon by governments reflects too small a cut in emissions to prevent "dramatic impacts" on the world's oceans, with lead author Jean-Pierre Gattuso remarking that "The ocean has been minimally considered at previous climate negotiations. Our study provides compelling arguments for a radical change at the UN conference (in Paris) on climate change". The rate at which ocean acidification will occur may be influenced by the rate of surface ocean warming, because the chemical equilibria that govern seawater pH are temperature-dependent. Greater seawater warming could lead to a smaller change in pH for a given increase in CO2.
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" – Pope Francis lauded Kohl as "a great statesman and committed European [who] worked with farsightedness and devotion for the good of the people in Germany and in neighbouring European countries." – Hungarian Prime Minister Viktor Orbán called Kohl the "great old man" of European politics and "Hungary’s friend". – Italian President Sergio Mattarella called Kohl one of Europe's founding fathers, and said that "he who was, rightly, described as 'the Chancellor of Reunification', worked with far-sightedness and determination, in years marked by deep and epochal changes in world equilibria, to give back unity to his country in the framework of the great project of European integration. As an authentic statesman, he knew how to combine pragmatism and a capacity of vision, furnishing a courageous contribution not only to the fall of the Berlin Wall and the reunification of Germany, but also to overcoming the dramatic divisions which, for decades, had torn Europe.
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This is in contrast to cladogenesis—or speciation in a sense—in which a population is split into two or more reproductively isolated groups and these groups accumulate sufficient differences to become distinct species. The punctuated equilibria hypothesis suggests that anagenesis is rare and that the rate of evolution is most rapid immediately after a split which will lead to cladogenesis, but does not completely rule out anagenesis. Distinguishing between anagenesis and cladogenesis is particularly relevant in the fossil record, where limited fossil preservation in time and space makes it difficult to distinguish between anagenesis, cladogenesis where one species replaces the other, or simple geographic immigration/emigration patterns. Recent evolutionary studies are looking at anagenesis and cladogeneis for possible answers in developing the hominin phylogenetic tree to understand morphological diversity and the origins of Australopithecus anamensis, and this case could possibly show anagenesis in the fossil record.
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The IS curve moves to the right, causing higher interest rates (i) and expansion in the "real" economy (real GDP, or Y) The IS–LM model, or Hicks–Hansen model, is a two-dimensional macroeconomic tool that shows the relationship between interest rates and assets market (also known as real output in goods and services market plus money market). The intersection of the "investment–saving" (IS) and "liquidity preference–money supply" (LM) curves models "general equilibrium" where supposed simultaneous equilibria occur in both the goods and the asset markets. Yet two equivalent interpretations are possible: first, the IS–LM model explains changes in national income when price level is fixed short-run; second, the IS–LM model shows why an aggregate demand curve can shift. Hence, this tool is sometimes used not only to analyse economic fluctuations but also to suggest potential levels for appropriate stabilisation policies.
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The turnpike model of money explains valued money as a way to facilitate trade between agents who meet as strangers in spatially separated isolated markets with no communication or transactions between the markets at any time. In the standard frictionless Arrow-Debreu model, since the nonmonetary competitive equilibria are already Pareto optimal, money can't facilitate exchange or is at best useless. A common approach in monetary economics is to either require that agents hold money for institutional reasons (for example, to pay taxes, or because the government forces individuals to accept it), to enter money holdings directly into individual's utility functions (the so-called "money in utility" or Sidrauski model), or to impose an arbitrary Cash-in-advance constraint (the so-called Clower constraint). However all of these approaches are somewhat ad hoc and do not explain why intrinsically worthless money can have value as medium of exchange.
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The dotted line in Figure 1 shows the optimal probability that player Y plays 'Stag' (in the y-axis), as a function of the probability that player X plays Stag (shown in the x-axis). In Figure 2 the dotted line shows the optimal probability that player X plays 'Stag' (shown in the x-axis), as a function of the probability that player Y plays Stag (shown in the y-axis). Note that Figure 2 plots the independent and response variables in the opposite axes to those normally used, so that it may be superimposed onto the previous graph, to show the Nash equilibria at the points where the two player's best responses agree in Figure 3. There are three distinctive reaction correspondence shapes, one for each of the three types of symmetric 2x2 games: coordination games, discoordination games and games with dominated strategies (the trivial fourth case in which payoffs are always equal for both moves is not really a game theoretical problem).
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Gravitational accelerations at The and points lie at the third corners of the two equilateral triangles in the plane of orbit whose common base is the line between the centers of the two masses, such that the point lies behind () or ahead () of the smaller mass with regard to its orbit around the larger mass. The triangular points ( and ) are stable equilibria, provided that the ratio of is greater than 24.96.Actually ≈ , Neil J. Cornish with input from Jeremy Goodman This is the case for the Sun–Earth system, the Sun–Jupiter system, and, by a smaller margin, the Earth–Moon system. When a body at these points is perturbed, it moves away from the point, but the factor opposite of that which is increased or decreased by the perturbation (either gravity or angular momentum-induced speed) will also increase or decrease, bending the object's path into a stable, kidney bean-shaped orbit around the point (as seen in the corotating frame of reference).
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He cowrote a book on his pioneering research in the chemistry of metal chelate compounds with Nobel Laureate Melvin Calvin, and wrote or edited fourteen other textbooks that are in use by hundreds of chemists and biologists, including works on Critical Stability Constants (six volumes, with R.M. Smith), The Determination and Use of Stability Constants (with R.J. Motekaitis) and Metal COmplexes in Aqueous Solutions (with R.D. Hancock). Martell also authored over 550 articles that were published in peer-reviewed scientific journals, most of which dealt with equilibria, kinetics, and the physical properties of metal chelates, macrocyclic complexes and cryptates. In 1993, he, Motekaitis and Smith developed the first computer database to track the reaction rates of ligands and how they react with ions to form complex chemical compounds. After stepping down as department head in 1980, Martell served as a Distinguished Professor of Chemistry at Texas A&M; and continued his research.
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Mirjordavi N., Kazemeini M., R. Kharrat R., Ghazanfari M.H., Salehi A., Experimental Investigation of Gas-Heavy Oil Molecular Diffusion Coefficient in Porous Media: Experimental Results for CO2 in Iranian Crudes, journal of Defect and Diffusion Forum Vols. 312-315 (2011) pp 1049–1054, April 2011. 77\. Naseryan Moghadam, J., Salahshoor, K., Kharrat, R.: Intelligent Prediction of Porosity and Permeability from Well Logs for One of the Iranian Fractured Carbonate Reservoirs, J. Petroleum Science & Technology, Vol. 29, issue 20, 2095 - 2112, August 2011. 78\. Tavakkoli M. Masihi M., Ghazanfari M. H., Kharrat R., An improvement of thermodynamic Micellization model for prediction of asphaltene precipitation during gas injection in heavy crude, Fluid Phase Equilibria, June 2011, 308 (2011) 153– 163. 79\. Fatemia S.M., Kharrat R. & Vossoughi S.: Investigation of the Effect of Geometrical Properties of Networked Fractures on the Efficiency of Steam-Assisted Gravity Drainage Process, Vol 29, Issue 16, 2011, pp. 1625–1636. 80\.
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In game theory, the centipede game, first introduced by Robert Rosenthal in 1981, is an extensive form game in which two players take turns choosing either to take a slightly larger share of an increasing pot, or to pass the pot to the other player. The payoffs are arranged so that if one passes the pot to one's opponent and the opponent takes the pot on the next round, one receives slightly less than if one had taken the pot on this round. Although the traditional centipede game had a limit of 100 rounds (hence the name), any game with this structure but a different number of rounds is called a centipede game. The unique subgame perfect equilibrium (and every Nash equilibrium) of these games indicates that the first player take the pot on the first round of the game; however, in empirical tests, relatively few players do so, and as a result, achieve a higher payoff than the payoff predicted by the equilibria analysis.
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In 1885, Eugene Goldstein named the cathode ray, later discovered to be composed of electrons, and the canal ray, later discovered to be positive hydrogen ions that had been stripped of their electrons in a cathode ray tube; these would later be named protons. The year 1885 also saw the publishing of J. H. van 't Hoff's L'Équilibre chimique dans les Systèmes gazeux ou dissous à I'État dilué (Chemical equilibria in gaseous systems or strongly diluted solutions), which dealt with this theory of dilute solutions. Here he demonstrated that the "osmotic pressure" in solutions which are sufficiently dilute is proportionate to the concentration and the absolute temperature so that this pressure can be represented by a formula which only deviates from the formula for gas pressure by a coefficient i. He also determined the value of i by various methods, for example by means of the vapor pressure and François-Marie Raoult's results on the lowering of the freezing point.
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Livy X 29, 12-17; nefando sacro, mixta hominum pecudumqur caedes, "by an impious rite, a mixed slaughter of people and flock" 39, 16; 42, 6-7. More recently Dario Sabbatucci has given a different interpretation of the meaning of Stator within the frame of his structuralist and dialectic vision of Roman calendar, identifying oppositions, tensions and equilibria: January is the month of Janus, at the beginning of the year, in the uncertain time of winter (the most ancient calendar had only ten months, from March to December). In this month Janus deifies kingship and defies Jupiter. Moreover January sees also the presence of Veiovis who appears as an anti-Jupiter, of Carmenta who is the goddess of birth and like Janus has two opposed faces, Prorsa and Postvorta (also named Antevorta and Porrima), of Iuturna, who as a gushing spring evokes the process of coming into being from non-being as the god of passage and change does.
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47-56 and separate them from irradiated targets, which he did at Orsay. To conduct most of his research he developed the methodology for studying species and equilibria between species in extremely diluted solutions (which radioactivity allows until about 10−14 M), and he pushed, at the theoretical level, the description of the thermodynamic behaviour of a few atoms in terms of deviation from the law of mass action,A. Peneloux, R. Guillaumont, « Solutions de dilution extrême et loi d’action de masse », CR Acad. Sci. Paris, 1990, 310 (12), p. 1607-1613 which gave a foundation to chemical experiments on elements 6d (Z>103), produced atom by atom by radiochemists at accelerators.J.P. Adloff et R. Guillaumont, Fundamental of Radiochemistry, CRC Press, 1993 At the same time, he participated in the study of thermodynamicF David, K Samhoun, R. Guillaumont, N. Edelstein, «Thermodynamic properties of 5f elements », Journal of Inorganic and Nuclear Chemistry, 1978, 40 (1), p. 69-74R.
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Generally speaking, risk-neutral pricing in structural models of financial interconnectedness requires unique equilibrium prices at maturity in dependence of the exogenous asset price vector, which can be random. While financially interconnected systems with debt and equity cross- ownership without derivatives are fairly well understood in the sense that relatively weak conditions on the ownership structures in the form of ownership matrices are required to warrant uniquely determined price equilibria, the Fischer (2014) model needs very strong conditions on derivatives – which are defined in dependence on any other liability of the considered financial system – to be able to guarantee uniquely determined prices of all system-endogenous liabilities. Furthermore, it is known that there exist examples with no solutions at all, finitely many solutions (more than one), and infinitely many solutions. At present, it is unclear how weak conditions on derivatives can be chosen to still be able to apply risk-neutral pricing in financial networks with systemic risk.
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Following his largely experimental studies in his doctoral and postdoctoral research, his interests turned increasingly to the application of statistical mechanics to problems in chemical engineering and applied physics. Much of chemical engineering involves the handling and processing of dense fluids and liquids, so that a knowledge of their thermodynamic and transport behaviour is essential to design of process equipment. It was to these areas that he addressed himself, and he has been largely responsible for the introduction of statistical mechanics and atomistic simulation methods (Monte Carlo and molecular dynamics) into chemical engineering. His research has focused on the development of reliable predictive methods based in statistical mechanics for phase and chemical equilibria for mixtures; equations of state for complex fluid mixtures, particularly those involving associating liquids and polymers; thermodynamics, transport in interfaces, including small droplets, gas-liquid and liquid-liquid interfaces and nano-porous media; prediction of viscosity, diffusion coefficients, and thermal conductivities; natural gas storage in porous media.
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The religious meaning of the vow is in both cases an appeal to the supreme god by a Roman chief at a time of need for divine help from the supreme god, albeit for different reasons: Fabius had remained the only political and military responsible of the Roman State after the devotio of P. Decius Mus, Papirius had to face an enemy who had acted with impious rites and vows, i.e. was religiously reprehensible.Livy X 29, 12–17; nefando sacro, mixta hominum pecudumque caedes, "by an impious rite, a mixed slaughter of people and flock" 39, 16; 42, 6–7. More recently Dario Sabbatucci has given a different interpretation of the meaning of Stator within the frame of his structuralistic and dialectic vision of Roman calendar, identifying oppositions, tensions and equilibria: January is the month of Janus, at the beginning of the year, in the uncertain time of winter (the most ancient calendar had only ten months, from March to December).
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Reactions are known where the deuterated species reacts faster than the undeuterated analogue, and these cases are said to exhibit inverse kinetic isotope effects (IKIE). IKIE's are often observed in the reductive elimination of alkyl metal hydrides, e.g. (Me2NCH2CH2NMe2)PtMe(H). In such cases the C-D bond in the transition state, an agostic species, is highly stabilized relative to the C–H bond. An inverse effect can also occur in a multistep reaction if the overall rate constant depends on a pre- equilibria prior to the rate-determining step which has an inverse equilibrium isotope effect. For example, the rates of acid-catalyzed reactions are usually 2-3 times greater for reactions in D2O catalyzed by D3O+ than for the analogous reactions in H2O catalyzed by H3O+ This can be explained for a mechanism of specific hydrogen-ion catalysis of a reactant R by H3O+ (or D3O+). :H3O+ \+ R RH+ \+ H2O :RH+ \+ H2O → H3O+ \+ P The rate of formation of products is then d[P]/dt = k2[RH+] = k2K1[H3O+][R] = kobs[H3O+][R].
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In control of stochastic multi-agent systems, Zhang thoroughly studied the interaction of interest coupled decision-makers and the uncertainty of individual behavior, which is the prominent characteristic of multi-agent systems (MASs). He made a systematic study of the sample path behavior of the closed-loop system in relation to Nash Equilibria (NE) and a substantial contribution to the developing theory of Nash Certainty Equivalence (NCE) for large population stochastic dynamic games. He introduced the concepts of asymptotic Nash- equilibrium in probability and almost surely, and elucidated the relationship between these concepts, which provides necessary tools for analyzing the optimality of the decentralized control laws. With respect to the decentralized quadratic-type and tracking-type performance indices, by using Nash Certainty Equivalence he developed decentralized optimal controls, and proved the optimality of the closed-loop systems. He also initiated the study on consensusability and formability of MAS and obtained necessary and sufficient conditions which reflect the intrinsic relationships between the consensusability/formability and the agents’ dynamics, admissible control sets and communication topologies.
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For a Lewis acid, its affinity for a hydride ligand is called its hydricity: :MLnHn− ⇌ MLn(n+1)− \+ H− Since hydride does not exist as a stable anion in solution, this equilibrium constant (and its associated free energy) are calculated from measurable equilibria. The reference point is the hydricity of a proton, which in acetonitrile solution is calculated at −76 kcal mol−1: :H+ \+ H− ⇌ H2 Relative to a proton, most cations exhibit a lower affinity for H−. Some examples include: :[Ni(dppe)2]2+ \+ H− ⇌ [HNi(dppe)2]+ ΔG298 = −63 kcal mol−1 :[Ni(dmpe)2]2+ \+ H− ⇌ [HNi(dmpe)2]+ ΔG298 = −50.7 kcal mol−1 :[Pt(dppe)2]2+ \+ H− ⇌ [HPt(dppe)2]+ ΔG298 = −53 kcal mol−1 :[Pt(dmpe)2]2+ \+ H− ⇌ [HPt(dmpe)2]+ ΔG298 = −42.6 kcal mol−1 These data suggest that [HPt(dmpe)2]+ would be a strong hydride donor, reflecting the relatively high stability of [Pt(dmpe)2]2+.M Tilset "Organometallic Electrochemistry: Thermodynamics of Metal–Ligand Bonding" in Comprehensive Organometallic Chemistry III, Eds Crabtree, R. H.; Mingos, D. M. P. 2007 Elsevier. . The ionic bond character in transition metal hydrides can be measured for D ligands via deuterium quadrupole coupling constants.
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In a capitalist society, the human perception that "the market" is an independent, sentient entity, is how buyers, sellers, and producers naturalise market exchange (the human choices and decisions that constitute commerce) as a series of "natural phenomena ... that ... happen of their own accord". Such were the political-economy arguments of the economists whom Karl Marx criticized when they spoke of the "natural equilibria" of markets, as if the price (value) of a commodity were independent of the volition and initiative of the capitalist producers, buyers, and sellers of commodities. In the 18th century, the Scottish social philosopher and political economist Adam Smith, in The Wealth of Nations (1776) proposed that the "truck, barter, and exchange" activities of the market were corresponding economic representations of human nature, that is, the buying and selling of commodities were activities intrinsic to the market, and thus are the "natural behaviour" of the market. Hence, Smith proposed that a market economy was a self-regulating entity that "naturally" tended towards economic equilibrium, wherein the relative prices (the value) of a commodity ensured that the buyers and sellers obtained what they wanted for and from their goods and services.
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One game in which the backward induction solution is well known is tic-tac-toe, but in theory even Go has such an optimum strategy for all players. The problem of the relationship between subgame perfection and backward induction was settled by Kaminski (2019), who proved that a generalized procedure of backward induction produces all subgame perfect equilibria in games that may have infinite length, infinite actions as each information set, and imperfect information if a condition of final support is satisfied. The interesting aspect of the word "credible" in the preceding paragraph is that taken as a whole (disregarding the irreversibility of reaching sub-games) strategies exist which are superior to subgame perfect strategies, but which are not credible in the sense that a threat to carry them out will harm the player making the threat and prevent that combination of strategies. For instance in the game of "chicken" if one player has the option of ripping the steering wheel from their car they should always take it because it leads to a "sub game" in which their rational opponent is precluded from doing the same thing (and killing them both).
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