176 research outputs found

    Optimization of a Third-Order Gradiometer for Operation in Unshielded Environments

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    The optimum geometry of a third-order gradiometer for operation in unshielded environments is discussed. The optimization result depends on the specific signal and noise conditions. The fetal heart is considered as an example of the signal source. We optimized the gradiometer such that the signal-to-noise ratio is maximized in an averaged sense for all relevant environmental noise conditions and distances to the signal source. The resulting design consists of two second-order gradiometers that can be combined to form a third-order gradiometer in noisy environments, whereas a single second-order gradiometer can be used in low-noise environments. The gradiometer can provide the signal-to-noise ratio that allows detection of fetal heart signals in all relevant environmental noise conditions

    Cycle-preserving extension of demand functions to new commodities

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    A method is given to extend demand functions to new commodities under preservation of the cycle number, i.e. the minimal length of a preference cycle revealed by the demand function. Thus, Gale's (Economica, N.S., 1960, 27, 348–354) demand function that shows that the weak axiom of revealed preference does not imply the strong axiom of revealed preference for three commodities can be extended to more than three commodities. Also Shafer's (Journal of Economic Theory, 1977, 16, 293–309) result, that arbitrarily high cycle numbers exist for three commodities, can now be extended to any number of commodities larger than three. This completely settles a question raised by Samuelson (Economica, N.S., 1953, 20, 1–9)

    A note on partial vertical integration

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    A simple model is constructed to show how partial vertical integration may emerge as an equilibrium market structure in a world characterized by rationing, differences in the reservation prices of buyers, and in the risk attitudes of buyers and sellers. The buyers with the high reservation prices turn out to be vertically integrated

    Perceptrons.

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