Essential gyrators and reciprocity in junction structures

This paper proposes an extended definition of reciprocity for a multiport junction structure based on the concept of essential gyrator coupling. Two theorems are given for junction structures containing gyrators and an algorithm is presented for identifying essential gyrators. The results are useful both theoretically and for designing efficient computation procedures for junction structures.     

The graph-theoretic field model—I. Modelling and formulations

The Graph-Theoretical Field Model provides a unifying approach for developing numerical models of field and continuum problems. The methodology examines the field problem from the first stages of conceptualization without recourse to the governing differential equations of the field problem; this is accomplished by deriving discrete statements of the physical laws which govern the field behaviour. There are generally three laws, and these are modelled by the “cutset equations”, the “circuit equations”, and the “terminal equations”. In order to establish these three sets of equations it is expedient first to spatially discretize the field in a manner similar to the finite difference method and then to associate a linear graph (denoted as the field graph) with the spatial discretization. The concept of “through” and “across” variables, which underlies the cutset and circuit equations respectively, enables one to define the graph in an unambiguous manner such that each “edge” of the graph identifies a pair of complementary variables. From a knowledge of the constitutive properties and the boundary conditions of the field it is possible to associate terminal equations with sets of edges. Since the resulting sets of equations represent the field equations, these equations provide the basis for a complete (but approximate) solution to the field or continuum problem. In fact, this system approach uses a two part model: one for the components and another for the interconnection pattern of the components which renders the formulation procedures totally independent of the solution procedure.This paper presents the theoretical basis of the model and several graph-theoretic formulations for steady-state problems. Examples from heat conduction and small- deformation elasticity are included.     

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.     

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.     

Effects of perceptual salience on the matrix task performance of four- and six-year-old children.

The effects of salience on 4- and 6-year-old children's ability to classify multiplicatively was investigated. A rank-ordered salience hierachy consisting of 3 dimensions was first assessed for each S. Several weeks later half the Ss of each age group were presented with a series of 9 3 times 3 matrix problems consisting of values from 2 dimensions ranked high in salience. The remaining half received identically structured matrices consisting of values from 1 highly salient dimension and of others from a dimension ranked low in salience. The goal in each problem was to select that compound stimulus from a set of alternatives that appropriately filled an empty cell in the matrix. Prior to the matrix problems, half the Ss in each matrix condition received sensitization training designed to increase the salience of the relevant dimensions in the matrix problems. The results showed that the pre-assessed salience of the relevant dimensions affected matrix solution in that more accurate performance was associated with those problems with both relevant dimensions relatively high in salience than those with one high and one low. Although the older Ss solved more problems, the evidence for coordination in the younger Ss was clear. No effects of sensitization training were found.