Water-clocks and time measurement in classical antiquity

The water-clock was the first mechanical device for time measurement to be used by the Greeks. Previously they had relied on sundials, or observation of the phases of the moon or the position of the sun in the zodiac to locate points of time within the day, month or year; and by the mid-fifth century BC they had made some progress with the difficult calendar problems due to the fact that the solar day, the lunar month, and the solar year are not commensurable with each other in whole numbers.     

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.     

On Linear Least-Squares Estimators for Continous-Time Stochastic Systems

The problem of least-squares state estimation of stochastic continuous-time linear systems is reconsidered. A concise derivation of the least-squares minimal-order estimator is presented using an innovations approach. An important result is the reinstatement of the problem in a least-squares estimation framework independent of deterministic observer theory. A second result is thus the clarification of previous approaches to the problem, particularly in relation to observer theory.