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...dratic function|two]], is a simple and accessible demonstration of [[chaos theory|chaos]] in [[dynamical system]]s. It can be constructed by performing the f ...x_number#Polar_complex_plane|argument]] (angle) is not a [[rational number|rational]] multiple of π, ...

...'' {{=}} 2}}}} but there are multiple such roots and there is no canonical choice among them.<ref>{{harvnb|Robert|2000|p=252}}</ref> ...''p''</sub>&nbsp;&lt;&nbsp;1 to all of {{SubSup|'''C'''|''p''|×}} for each choice of log_''p''(''p'') in '''C'''_''p''.<ref>{{harvnb|Cohe ...

...t valued [[solution concept]] in [[game theory]] that relaxes the rational choice assumptions of perfect maximization ("no mistakes") and perfect beliefs ("n |title= M Equilibrium: A dual theory of beliefs and choices in games ...

...has that cohomology ring; except in the simplest cases, there exist other rational homotopy types with the same cohomology ring which are not formal. ...t3=Morgan |first3=John |last4=Sullivan |first4=Dennis |title=Real Homotopy Theory of Kähler Manifolds |journal=Inventiones Mathematicae |date=1975 |volume=29 ...

...an Theorem: A Simpler Proof and Some Ethical Connotations |date=1992 |work=Rational Interaction: Essays in Honor of John C. Harsanyi |pages=305–319 |editor-las ...a weighted sum of individual [[utility function]]s, so long as the social choice function satisfies three conditions:<ref name=":0" /> ...

{{Short description|Concept in decision theory}} {{ about|the treatment of probability in expected utility theory|the gambling uses of the term|Lottery }} ...

...l with respect to [[smash product]] and perhaps some other conditions; one choice is the category of [[symmetric spectrum|symmetric spectra]]</ref> category ...gory of commutative ring spectra over the field <math>\mathbb{Q}</math> of rational numbers is [[Quillen equivalent]] to the category of [[differential graded ...

...0121-3 |arxiv=math/9812034|s2cid=15720862 }}</ref> and [[rational homotopy theory]]. ...e this point the grading is written in superscript: <math>L^i</math>). The choice of cohomological grading usually depends upon personal preference or the si ...

...Yang–Mills connections on non-Kähler manifolds", ''Math. aspects of string theory'' (San Diego, Calif., 1986), Adv. Ser. Math. Phys. 1, 560&ndash;573, World The Inoue surface of type ''S''⁰ is determined by the choice of an integer matrix ''φ'', constrained as above. There is a countable numb ...

...=2017-07-22 | url-status=dead }}</ref> Since then it has become central to theory of motives. For every adequate equivalence relation, one may define the [[c ...lgebraic geometry)|divisor]]s modulo linear equivalence. All cycles modulo rational equivalence form the [[Chow ring]]. ...

...ly irrelevant}}</ref> is a [[probabilistic model]] used in [[social choice theory]] for analyzing [[Ranked voting|ranked]] [[Electoral system|voting method]] ...obabilities |title=Voting Paradoxes and Group Coherence |series=Studies in Choice and Welfare |year=2011 |last1=Gehrlein |first1=William V. |last2=Lepelley | ...

...ry of group schemes based on the notion of group functor instead of scheme theory. ...ry of sets satisfying the [[gluing axiom]]; the perspective known as the [[rational points#Definition|functor of points]]. Under this perspective, a group sche ...

...in \mathbb{N}}</math> be an [[Enumeration algorithm|enumeration]] of the [[rational number]]s in the [[unit interval]] {{math|[0, 1]}}. Let <math>\{a_j\}_{j \i ...hoice of <math>a_0</math>, we can assume <math>g(0)=0</math> and up to the choice of a multiplicative factor we can assume that {{mvar|g}} maps the interval ...

...h indefinite sums and indefinite integrals, it is valid up to an arbitrary choice of the [[constant of integration]]. Using [[operator algebra]] avoids clutt ==Choice of the constant term== ...

{{Short description|School of thought within decision theory}} ...author-link=Arif Ahmed (philosopher) |date=2021 |title=Evidential Decision Theory |publisher=Cambridge University Press |isbn=9781108607865}}</ref>{{rp|7}} ...

..., and they are related to the [[moduli of curves]]. Their [[Rational point|rational points]] are of interest for the study of the [[inverse Galois problem]], a ...bar\Q(T)</math> with Galois group <math>G</math>) then it is expected that rational points are related to regular extensions of <math>\Q(T)</math> with Galois ...

...n utility function. The theorem forms the foundation of [[expected utility theory]]. ...University Press, 1953.</ref> That is, they proved that an agent is (VNM-)rational ''if and only if'' there exists a real-valued function ''u'' defined by pos ...

...h the instantaneous-adjustment case). This dynamic equation is [[stability theory|stable]] provided the derivative of ''f'' with respect to ''P'' is negative ...Utility maximization problem|utility-maximizing]] [[Rational choice theory|rational agents]] can take the shape of any [[Function (mathematics)|function]] that ...

{{Short description|School of thought within decision theory}} ...irst=Arif |author-link=Arif Ahmed (philosopher) |title=Evidential Decision Theory |date=2021 |publisher=Cambridge University Press |isbn=9781108607865}}</ref ...

...f they would rather choose A than B. Preferences are central to [[decision theory]] because of this relation to behavior. Some methods such as [[Ordinal Prio ...Cayeux, I., Porcherot, C., & Sander, D. (2010). "I'm no longer torn after choice: How explicit choices can implicitly shape preferences for odors". ''Psycho ...