The DT-Polynomial Approach to Discrete Time-Varying Network Flow Problems

This paper introduces a polynomial operator called the DT-polynomial as a novel approach to network flow problems. The class of networks dealt with is time-varying in the sense that the capacity, cost, and travel-time of each edge may vary in discrete time. The Dt-polynomial is a polynomial in two operators, D (delay) and T (time), which is used for describing the time-varying transmission characteristics. The paper starts with the mathematics involving the DT-polynomials. A new shortest arrival route algorithm is presented, and its computational complexity is found to be favorable in comparison with others such as Dijkstra's method and the potential method derived from Ford-Fulkerson's technique. Furthermore, a dynamic flow problem is formulated and analyzed in terms of DT-polynomials, and a latest-departure earliest-arrival schedule is given. Finally, a modified DT-polynomial is applied to digital filter networks.     

Stability analysis of nonlinear control systems with characteristics equations having complex coefficients

In this paper, the stability equation method is applied to the analysis of nonlinear systems with characteristics equations having complex coefficients. Three types of systems are studied: those with unstable open-loop poles, unstable characteristics roots or an equal number of open-loop poles and zeros.     

The elimination of hypo from photographic images

It is very difficult, if not impossible, to remove the last traces of hypo from photographic papers by any known procedure of washing. The sulfur in the residual hypo ultimately, and especially under abnormal conditions of temperature and humidity, combines with the silver image to form yellowish brown silver sulfide. This phenomenon is known as sulfiding or “fading” of the image. The various factors which affect the rate of fading of images and the washing out of hypo from films and papers are outlined.Chemical methods of hypo elimination have been proposed from time to time but the majority of these have not been satisfactory because they tend to leave substances such as thionates in the photographic material, which are equally as difficult to wash out as hypo and which also tend to sulfide or fade the silver image. A new hypo eliminator is recommended consisting of two volatile chemicals, hydrogen peroxide and ammonia. This eliminator oxidizes the hypo to sodium sulfate, which is inert and soluble in water, while any excess eliminator evaporates on drying.Two formulas and treatments are proposed: (1) Complete elimination of hypo for use by the professional, advanced amateur, and photofinisher who demand the highest standard of photographic quality in their prints.(2) Almost complete elimination of hypo (less than o.oi milligram per square inch).Since the conditions to which prints will be subjected are rarely known in advance, use of the “complete elimination treatment” is advised in all cases.