Error Estimation in Numerical Inversion of Laplace Transforms Using Padé Approximation

Uniform asymptotic estimates for the error in the main diagonal and first two subdiagonal Padé approximants for exp(iz) in a sector covering the real z axis are derived. The results are applied to analyze the error in a cerain procedure for the numerical inversion of the Laplace transform.     

Mirrow reactions of Down's syndrome infants and toddlers: cognitive underpinnings of self-recognition.

To examine the developmental significance of mirrow self-recognition in early childhood, a cross-sectional study with 55 Down's syndrome children was conducted. When their image is altered by rouge on the nose, normal infants by 22 months indicate self-recognition by touching their noses while looking in the mirror. Only a small percentage of Down's syndrome children touched their noses by this age, confirming the expected lag in this development. However, those young Down's syndrome infants with near-normal development quotient did manifest the reaction. In general, when developmental age was equated, the Down's syndrome children showed parallel development to normal children.     

Developmental priority of identity conservation: acceleration of identity and equivalence in normal and moderately retarded children

In an attempt to clarify the chronological relationship between identity and equivalence conservation, normal preschool-aged children (experiment 1) were exposed to brief videotape demonstrations of a model conserving identity and equivalence, identity only, equivalence only, or neither. Subsequent performances indicate that identity was easier to accelerate than equivalence, and training in both identity and equivalence appeared to be most effective in accelerating conservation. Trainable mentally retarded (TMR) children were then exposed to either the identity-equivalence-conserving or control model (experiment 2). This population, which some have argued remains at a preoperational level of functioning, was more likely to conserve identity than equivalence. In addition, conservation in the training group increased following training, though these gains were not maintained over a 3-week retention interval.     

Sex-related differences in response to practice on a visual-spatial test and generalization to a related test

93 first graders (mean age 6.5 years) were given a pretest and posttest on half of the items from the Children's Embedded Figures Test. Half of the children were randomly assigned to a training condition and received a brief training procedure on visual-spatial disembedding prior to the administration of the posttest. Children in the control condition received no training. The performance of girls improved significantly more from pretest to posttest than the performance of boys. Boys and girls showed similar beneficial effects of training in addition to the benefit of direct practice. The tendency that was observed for boys to perform higher than girls on the pretest, p less than .10, was not evident on the posttest. Scores on the pretest predicted scores on a different measure of visual-spatial ability only for children in the control group. The results are interpreted in terms of current theories of sex differences in visual-spatial perception.