There have been several recent studies concerning feedforward networks and the problem of approximating arbitrary functionals of a finite number of real variables. Some of these studies deal with cases in which the hidden-layer nonlinearity is not a sigmoid. This was motivated by successful applications of feedforward networks with nonsigmoidal hidden-layer units. This paper reports on a related study of radial-basis-function (RBF) networks, and it is proved that RBF networks having one hidden layer are capable of universal approximation. Here the emphasis is on the case of typical RBF networks, and the results show that a certain class of RBF networks with the same smoothing factor in each kernel node is broad enough for universal approximation.

This paper concerns conditions for the approximation of functions in certain general spaces using radial-basis-function networks. It has been shown in recent papers that certain classes of radial-basis-function networks are broad enough for universal approximation. In this paper these results are considerably extended and sharpened.

A particular time‐varying network consisting of several parallel transmission paths, each containing input and output modulators, is described and analyzed. It is shown that, under certain conditions, the network may be characterized by a transfer function. A particular form of this transfer function yields periodic filtering characteristics over a limited frequency band without employing distributed elements. Techniques are also presented for realizing highly selective band‐pass filters without the use of magnetic elements. Some practical applications are discussed in detail and experimental verification is presented.

It is proved that a condition similar to the Nyquist criterion guarantees the stability (in an important sense) of a large class of feedback systems containing a single time‐varying nonlinear element. In the case of principal interest, the condition is satisfied if the locus of a certain complex‐valued function (a) is bounded away from a particular disk located in the complex plane, and (b) does not encircle the disk.

Let ON denote the set of N-vector-valued