Zeroes expenditure represent a difficulty in the analysis of household survey data. Zero expenditures are the result of two phenomena: nonconsumption and infrequency of purchase. Distinguishing between these types of zeroes is difficult in the kinds of data of interest to agricultural economists. This paper proposes a novel approach that yields less biased estimates of latent expenditure when t...

In part I it was shown that for each k ≥ 1 the generalized Sato–Levine invariant detects a gap between k-quasi-isotopy of link and peripheral structure preserving isomorphism of the finest quotient Gk of its fundamental group, ‘functorially’ invariant under k-quasi-isotopy. Here we show that Cochran’s derived invariant β, provided k ≥ 3, and a series of μ̄-invariants, starting with μ̄(111112122) ...

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Many authors have studied methods of generalising Steiner quasigroups by using certain cycle systems. The usual aims have been to preserve the law (xy)y = x, by using the standard construction, or to preserve the law xy = yx, by using the opposite vertex construction. In this paper we seek to generalise the law (xy)y = x to laws of the form ( ... (xy)y . . . )y = x and (y( ... (y(yx)) ... ) = x...

Engel structures on M×S and M×I are studied in this paper, where M is a 3–dimensional manifold. We suppose that these structures have characteristic line fields parallel to the fibres, S or I . It is proved that they are characterized by contact structures on the cross section M , the twisting numbers, and Legendrian foliations on both ends M × ∂I in the case of M × I . AMS Classification 57R25...

OBJECT The authors conducted a study to determine seizure-related outcomes in a group of pediatric patients with pathologically proven focal cortical dysplasia (FCD) treated by focal cortical resections and multiple subpial transections (MSTs). METHODS The authors performed a retrospective review of pediatric patients in whom surgery was conducted to treat medically refractory epilepsy second...