Interestingly, this fact can be used to perform corresponding sampling tasks from another set of states : so-called classical states, whose the optical equivalence theorem.
12.
*PM : unit disk upper half-plane conformal equivalence theorem, id = 4279-- WP guess : unit disk upper half-plane conformal equivalence theorem-- Status:
13.
*PM : unit disk upper half-plane conformal equivalence theorem, id = 4279-- WP guess : unit disk upper half-plane conformal equivalence theorem-- Status:
14.
This result is known as the " Dahlquist equivalence theorem ", named after Germund Dahlquist; this theorem is similar in spirit to the Lax equivalence theorem for finite difference methods.
15.
This result is known as the " Dahlquist equivalence theorem ", named after Germund Dahlquist; this theorem is similar in spirit to the Lax equivalence theorem for finite difference methods.
16.
If the left side of the equation is to be interpreted as an expectation value in the Hilbert space with respect to an operator, then in the context of quantum optics this equation is known as the optical equivalence theorem . ( For details on the properties and interpretation of the Wigner function, see its main article .)
17.
The compass is assumed to collapse when lifted from the page, so may not be directly used to transfer distances . ( This is an unimportant restriction since, using a multi-step procedure, a distance can be transferred even with collapsing compass; see compass equivalence theorem . ) More formally, the only permissible constructions are those granted by Euclid's first three postulates.
18.
The compass is assumed to collapse when lifted from the page, so may not be directly used to transfer distances . ( This is an unimportant restriction since, using a multi-step procedure, a distance can be transferred even with collapsing compass, see compass equivalence theorem . ) More formally, the only permissible constructions are those granted by Euclid's first three postulates.
19.
This condition in turn yields Myerson's ( 1981 ) celebrated revenue equivalence theorem : the expected revenue generated in an auction in which bidders have independent private values is fully determined by the bidders'probabilities y ^ { \ ast } \ left ( t \ right ) of getting the object for all types t as well as by the expected payoffs V ( \ underline { t } ) of the bidders'lowest types.
20.
While these authors derived and exploited the envelope theorem by restricting attention to ( piecewise ) continuously differentiable choice rules or even narrower classes, it may sometimes be optimal to implement a choice rule that is not piecewise continuously differentiable . ( One example is the class of trading problems with linear utility described in chapter 6.5 of Myerson ( 1991 ) . ) Note that the integral condition ( 3 ) still holds in this setting and implies such important results as Holmstrom's lemma ( Holmstrom, 1979 ), Myerson's lemma ( Myerson, 1981 ), the revenue equivalence theorem ( for auctions ), the Green-Laffont-Holmstrom theorem ( Green and Laffont, 1979; Holmstrom, 1979 ), the Myerson-Satterthwaite inefficiency theorem ( Myerson and Satterthwaite, 1983 ), the Jehiel-Moldovanu impossibility theorems ( Jehiel and Moldovanu, 2001 ), the McAfee-McMillan weak-cartels theorem ( McAfee and McMillan, 1992 ), and Weber's martingale theorem ( Weber, 1983 ), etc . The details of these applications are provided in Chapter 3 of Milgrom ( 2004 ), who offers an elegant and unifying framework in auction and mechanism design analysis mainly based on the envelope theorem and other familiar techniques and concepts in demand theory.
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