Some Theorems in Group Velocity

Some Useful Network Theorems

Thévenin’s theorem is used to represent a part of a network by a voltage source Vt and a series impedance Zt , as shown in Fig. D.1. Figure D.1(a) shows a network divided into two parts, A and B. In Fig. D.1(b), part A of the network has been replaced by its Thévenin equivalent: a voltage source Vt and a series impedance Zt . Figure D.1(c) illustrates how Vt is to be determined: Simply open-cir...

Some Theorems on Coverings

Some Fixed Point Theorems

Introduction. We wish to summarize here some new asymptotic fixed point theorems. By an asymptotic fixed point theorem we mean roughly a theorem in functional analysis in which the existence of fixed points of a map ƒ is proved with the aid of assumptions on the iterates f of ƒ. Such theorems have proved of use in the theory of ordinary and functional differential equations (see [7], [8], [9] a...

Group velocity

A short and largely traditional review of the concept of group velocity, prepared for the forthcoming Encyclopedia of Nonlinear Science Waves often propagate as a packet, or group, within which there are several wave crests. A common illustration is given by the wave pattern formed when a stone is thrown into a pond. An axially symmetric ring of waves on the water surface propagates outwards as...

Some Structure Theorems for