Ladder realizations of multivariable positive real functions

Necessary and sufficient conditions are obtained for the realization of an m-variable positive real function (PRF) as the impedence function of a resistively-terminated ladder network of m lossless two-ports connected in cascade. Each two-port is a single-variable lossless ladder with all of its transmission zeros either at the origin or at finity. Conditions are also obtained when each of the two-ports is a Fujisawa-type lowpass ladder.     

Polynomial Root Clustering

A sequence of tests on derived polynomials to be strictly Hurwitz polynomials is shown to be equivalent to a given (typically real) polynomial having all its zeros in an open sector, symmetric with respect to the real axis, in the left half-plane. The number of tests needed is at most 1 + ?(ln k)/(ln 3)?, where k is the integer associated with the central angle π/k of the sector. An extension of this result on the sector as a region of root clustering is given which shows that only a limited number of tests are needed to verify that the roots are clustered in a region composed as the intersection of a set of primative (sector-like) regions. The results reported evolve from application of a collection of mappings on the complex plane defined by a particular collection of Schwarz-Christoffel transformations.     

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.     

Perceptual training of height and brightness seriation in kindergarten children.

A study of seriation was conducted from the perspective of Gibson's theory of perceptual development. Kindergarten children who evidenced little seriation of height or brightness were assigned to either 1 of 3 perceptual training conditions or to a fourth, control condition. Training consisted of nonreinforced same-different judgments to wooden dowels varying in height, or in brightness, or simultaneously in height and brightness. The theoretical rationale for this training was that it would facilitate perception of the stimulus dimension(s) on which the dowels differed. It was found that perceptual training did facilitate seriation, particularly if both the height and brightness dimensions varied simultaneously in training.