Order of reduction

Reduction of Order If one homogeneous solution, say, can be found by inspection or otherwise, an equation of lower order can be obtained by the substitution = yju,. The resultant equation must be satisfied by = constant or Ai = 0. Thus the equation will be of reduced order if the new variable L/ = A y,/ul) is introduced. 

Patterson CC, Settle M (1976) The reduction of orders of magnitude errors in lead analysis. In LaFleur PD (ed) Accuracy in trace analysis sampling, sample handling, analysis. NBS Special Publication 422, p. 321... 

Equation (2.56) is a linear second-order differential equation. It can be solved by reduction of order. Let... 

Readers may recall the discussions on SIL determination from the risk matrix in Clause 1.0.2 and Fig. VIII/1.0.2-1 where a matrix comprising various orders of risk reduction is shown and the intersection of consequence and likelihood gives the order of risk reduction needed through SIL. As shown in the example, the intersection called for a risk reduction of order 2, that is, minimum SIL2 will be necessary. Little is elaborated here following IS/IEC 61511-3 2003 Annex C. As indicated earlier, after risk analysis, various hazardous events are listed. Then, likelihood and severity impact are categorized as follows. 

The experimental results can satisfactorily be explained by invoking the Kondo effect with a critical temperature of T 30 K. This implies that the moment originating from the F, levels is partially quenched by the conduction electrons. A similar explanation has been proposed by Barbara et al. (1977) for the well established concentrated Kondo system CeAl2 at ambient pressure to explain the reduction of ordered moment. 

One obtains the following rate expression for the kinetic of reduction of order n and varying with temperature. Thus, the rate of reduction or H2 consumption is [1]... 

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