Under general conditions, the equation g(x, y) = 0 implicitly defines y locally as a function of x. In this short note we study the combinatorial structure underlying a recently discovered formula for the divided differences of y expressed in terms of bivariate divided differences of g, by analyzing the number of terms an in this formula. The main result describes six equivalent characterizatio...

We propose a q-analog of classical plethystic conjectures due to Foulkes. In our conjectures, a divided difference of plethysms of Hall-Littlewood polynomials Hn(x; q) replaces the analogous difference of plethysms of complete homogeneous symmetric functions hn(x) in Foulkes’ conjecture. At q = 0, we get back the original statement of Foulkes, and we show that our version holds at q = 1. We dis...

This is a study of Favard interpolation—in which the nth derivatives of the interpolant are bounded above by a constant times the nth divided differences of the data—in the case the data is given on some subset of a rectangular lattice in R k. In some instances, depending on the geometry of this subset, we construct a Favard interpolant, and in other instances, we prove that none exists.

Four different age groups (8-9-year-olds, 11-12-year-olds, 13-15-year-olds and young adults) performed a spatial rule-switch task in which the sorting rule had to be detected on the basis of feedback or on the basis of switch cues. Performance errors were examined on the basis of a recently introduced method of error scoring for the Wisconsin Card Sorting Task (WCST; Barcelo & Knight, 2002). Th...

Reaction times (RTs) slow and become more variable with age. Research samples are typically small, biased, and of restricted age range. Consequently, little is known about the precise pattern of change, whereas evidence for sex differences is equivocal. The authors reanalyzed data for 7,130 adult participants in the United Kingdom Health and Lifestyle Survey, originally reported by F. A. Hupper...

Baiocchi et al. generalized a few years ago a classical theorem of Ingham and Beurling by means of divided differences. The optimality of their assumption has been proven by the third author of this note. The purpose of this note to extend these results to vector coefficient sums.

In this paper we derive a formula for divided differences of composite functions of several variables with respect to rectangular grids of points. Letting the points coalesce yields a chain rule for partial derivatives of multivariate functions. Math Subject Classification: 41A05, 65D05, 26A06

The present study examined age differences in executive functioning, using an externally cued task-switching paradigm. Two components of task switching were assessed: the ability to maintain and select among task sets (general switch costs) and the ability to switch between task sets (specific switch costs). In contrast to previous findings, we found large age-related differences in specific sw...

The effects of long-term and recent conjugal bereavement were investigated in a sample of 2,104 Swedish twins followed between 1984 and 1993. In co-twin-control analyses, the bereaved twin experienced significantly more depressive symptoms, more loneliness, and less life satisfaction than the married co-twin. This association existed for recently widowed (< 3 years) of both sexes. Long-term wid...

OBJECTIVES Two studies examined the extent to which the age-related positivity effect in autobiographical recall is the result of age differences in appraisal and memory. METHODS In Study 1, older and younger participants reported 1 pleasant and 1 unpleasant event for 5 days. Participants attempted to recall those events a week later. In Study 2, older and younger participants imagined that p...