Uniformly random tree generation

A simple procedure is described for generating a uniformly random tree in a given graph. The probability of obtaining such a tree in a complete graph is given together with the mean number of edge-set selections required and the associated variance.<>     

Digital-filter functions with fast coefficient implementation: an addendum

Five parallel transfer function formulations for digital filters are given. The coefficients in these allow a simple and very fast multiplication process. These functions provide a maximum bandwidth of about double that of an earlier set.     

Single-row routeing and planarity

The use of a Hamilton path within the graph of a network is considered as an aid to printed-circuit board mapping. It is shown that it may not be possible to augment a planar graph so that the resultant graph contains such a path and retains planarity.     

Interaction between process design and process control: economic analysis of process dynamics

A method is presented to assess the impact of disturbances on plant economic performance. The method is suitable for use during process design, and can be used to help evaluate alternative process structures or alternative control schemes for a given process. Non-linear steady-state optimization is performed to determine the best operating point in the absence of disturbances. Frequency response analysis of a linearized plant dynamic model is used to estimate the effects of plant disturbances on this ideal performance under a variety of control strategies. The method is illustrated on a case study involving minerals flotation circuit design.     

Alternative shortest paths in n-cubes

Explicit expressions are given for the number of shortest paths between any two vertices in an n-cube, each path being otherwise vertex disjoint from any specified shortest path between the same pair of vertices, and for the probability of randomly selecting one of these alternative paths     

Explicit form for input output function of linear time variable ladder networks

An explicit formulation is given for the input output voltage function of a general linear LCR ladder structure containing time variable elements. The expression is based on a recursive procedure which allows analysis by inspection.<>     

Shift register sequence segmentation using random segmentationpoints

Random choice of segment marker points in a shift register sequence provides a vanishingly small probability of segments overlapping if the number of shift register stages is sufficiently large     

Symmetrical state matrices for 2-element-kind networks

General state matrix formulations for CR, LR and LC networks which are, respectively, symmetrical, symmetrical and skew symmetrical are given.