Structural aspects of controllability and Sobservability—II. digraph decomposition

The graph theoretic aspects of controllability and observability are examined and related to the tensorial formulation of Part I of the paper. Particular emphasis is given to the significance of the system digraph decomposition and the relevance of this to certain system algebraic properties of interest in control theory.     

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.     

Self-regulation of timeout duration in the modification of disruptive classroom behavior

The effects of self-determination vs. teacher-determination of timeout duration on disruptive behavior were investigated in a group of 15 students in a special classroom who had learning disabilities and/or behavior problems. There were five phases to the study: In a repeated measures design each subject received timeout for 5 minutes, no timeout, 5 minutes timeout, selfdetermined timeout duration, and student = teacher-determined timeout duration. The overall effect of timeout was to reduce significantly the rate of disruptive behavior. The effects of various timeout conditions did not differ, indicating self-management of timeout duration was just as effective as when the teacher set the timeout duration.