Browsing by Subject "Differential information"

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Open Access
Effect of sample locations on computation of the exact scalar diffraction field (in English)
(IEEE, 2012) Esmer, G. B.; Özaktaş, Haldun M.; Onural, Levent
Computer generated holography is one of common methods to obtain three-dimensional visualization. It can be explained by behavior of propagating waves and interference. To calculate the scalar diffraction pattern on a hologram, there are myriad of algorithms in the literature. Some of them employ several approximations, so the calculated fields may not be the exact scalar diffraction field. However, there are algorithms to compute the exact scalar diffraction field with some limitations on the distribution of the given samples over the space. These algorithms are based on "field model" approach. The performance of an algorithm, based on field model, is investigated according to the distribution of given samples over the space. From the simulations, it was observed that the cumulative information provided by the given samples has to be enough to solve the inverse scalar diffraction field. The cumulative information can be increased by having more samples, but there are some scenarios that differential information obtained from the given samples can be infinitesimal, thus the exact diffraction field may not be computed. © 2012 IEEE.
Open Access
Theorems on the core of an economy with infinitely many commodities and consumers
(Elsevier BV, 2008) Evren, Ö.; Hüsseinov, F.
It is known that the classical theorems of Grodal [Grodal, B., 1972. A second remark on the core of an atomless economy. Econometrica 40, 581-583] and Schmeidler [Schmeidler, D., 1972. A remark on the core of an atomless economy. Econometrica 40, 579-580] on the veto power of small coalitions in finite dimensional, atomless economies can be extended (with some minor modifications) to include the case of countably many commodities. This paper presents a further extension of these results to include the case of uncountably many commodities. We also extend Vind's [Vind, K., 1972. A third remark on the core of an atomless economy. Econometrica 40, 585-586] classical theorem on the veto power of big coalitions in finite dimensional, atomless economies to include the case of an arbitrary number of commodities. In another result, we show that in the coalitional economy defined by an atomless individualistic model, core-Walras equivalence holds even if the commodity space is non-separable. The above-mentioned results are also valid for a differential information economy with a finite state space. We also extend Kannai's [Kannai, Y., 1970. Continuity properties of the core of a market. Econometrica 38, 791-815] theorem on the continuity of the core of a finite dimensional, large economy to include the case of an arbitrary number of commodities. All of our results are applications of a lemma, that we prove here, about the set of aggregate alternatives available to a coalition. Throughout the paper, the commodity space is assumed to be an ordered Banach space which has an interior point in its positive cone. © 2008 Elsevier B.V. All rights reserved.