Method of delays

Other mixed esters, eg, cellulose acetate valerate [55962-79-3] cellulose propionate valerate [67351-41-17, and cellulose butyrate valerate [53568-56-2] have been prepared by the conventional anhydride sulfuric acid methods (25). Cellulose acetate isobutyrate [67351-38-6] (44) and cellulose propionate isobutyrate [67351-40-0] (45) have been prepared with a 2inc chloride catalyst. Large amounts of catalyst and anhydride are required to provide a soluble product, and special methods of delayed anhydride addition are necessary to produce mixed esters containing the acetate moiety. Mixtures of sulfuric acid and perchloric acid are claimed to be effective catalysts for the preparation of cellulose acetate propionate in dichi oromethane solution at relatively low temperatures (46) however, such acid mixtures are considered too corrosive for large-scale productions. 

This method of delayed gel breaking has been reported for oxidative breaking and for enzyme gel breaking. Formulations of encapsulated gel breakers are shown in Table 17-14. Membranes for encapsulators are shown in Table 17-15. 

The phase space reconstruction of a time series is accomplished by the method of delays. An embedding dimension de is chosen, plus a time delay t°, and then the phase space is constructed using as variables y(t), y(t + t°),... 

The limit cycles corresponding to these oscillations can be obtained from a single experimental record (most conveniently, the thermocouple signal) using the method of delays . In this, the value of the signal at some time t is plotted against the value of the same signal at a later time t + where... 

Delayed Cross-Linkers. Chelated forms of the metals are much less reactive than the alkyl forms and, therefore, provide a method of delaying... 

In the method of delayed coincidences, the coincidence counting rate between detectors responding selectively to genetically related particles, e.g., a jS- or a-par-ticle and a y-ray or an electron or between y-rays, is plotted as a function of a time delay inserted in the electronic circuits used to detect one of them. The development of this method and of improved electronic techniques has led to the use of resolution times of between 10" and 10 sec. We shall not discuss these methods here, for they have been very adequately reported by Bell [i9], 2ff]. Further analysis of the experimental data has made it possible to measure lifetimes of the order of 10 sec. The limit to the method seems to be determined by the scintillating properties of the phosphor and its physical size. 

The first method, which was that used by Moon, who first detected the effect, made use of a Au source electroplated on to the periphery of a mechanical rotor. The details of both first and second methods have been summarized by Malmfors [i9]. The lifetime of the state can be calculated from the measured cross section for the process, the y-ray energy, and from the Doppler effect. It is instructive to compare the lifetimes obtained by different methods. The lifetime of the 411 kev state of Hg found by Graham and Bell by the method of delayed coincidences was (1.0 0.7) X10" sec that found by Moon and Davey by mechanical motion was (2.2 0.5) X10" sec by Malmfors (by heating), 3.5 X 10 sec and by Metzger and Todd , (2.2 0.2) X10 sec. In the same way, the lifetime of the 209 kev state of Hg found by Metzger and Todd ,... 

The lifetimes of F2 transitions in nuclei of intermediate atomic weight have usually proved too short to measure by the method of delayed coincidences. Of nine nuclei between Mg and Te, Coleman has succeeded in measuring the lifetime of only the first excited state of Te. The upper limits of the lifetimes of the rest are of the order of 10" sec. In heavier nuclei, the energies of the first... 

In olden times the lifetime distribution of short-lived nuclides was measured without a multichannel analyzer using the method of delayed coincidences. In this case, the start signals were delayed and the coincidence rate was plotted against the time of delay. The resulted graph showed the characteristic features of the exponential law, fi om which the decay constant could be determined by calculating the slope of the semilogarithmic (semilog) plot. 

For deep forming, it is therefore advisable to work in the as-quenched condition, say within 1 h after quenching for alloy 2024. The conventional method of delaying natural ageing for a number of days consists in maintaining the product at a low temperature, below -10 °C. 

It is also possible to apply the method of delayed coincidences to the measurement of the lifetimes of atoms which have been excited optically. This technique has the advantage that the very selective nature of the optical excitation process eliminates the effects of cascading discussed in section 6.3.4. In the past this method has been restricted to those levels which can be excited from the ground level by the absorption of intense re.sonance radiation. Thus only one or tv ro levels could be studied... 

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