Weighted norm

Such computational possibility may adopt the formal structure of a weighted norm ... 

Oxide Molecular weight Normative mineral Formula Molecular weight... 

Wt% " oxide of rock Molecular weight Molecular proportions Wt % CIPW norm Molecular weight Norm/ mol. wt Norm mol %)... 

NOTE Weight norms for infants, children, and adolescents are given in the sections on CHILDHOOD AND ADOLESCENT NUTRITION and INFANT DIET AND NUTRITION. 

Thus the //2-optimal eontroller minimizes the average magnitude of the sensitivity funetion weighted by fU(ja ), where fU(ja ) depends upon the speeifie input V(iuj). In mathematieal terms, the eontroller minimizes the 2-norm of the sensitivity funetion weighted by IV(iuj). 

With //oo-optimal control the inputs F(jw) are assumed to belong to a set of norm-bounded functions with weight fF(jw) as given by equation (9.125). Each input V(iuj) in the set will result in a corresponding error E(iuj). The i/oo-optimal controller is designed to minimise the worst error that can arise from any input in the set, and can be expressed as... 

In equation (9.131), sup is short for supremum, which means the final result is the least upper bound. Thus the //qo-optimal controller minimizes the maximum magnitude of the weighted sensitivity function over frequency range uj, or in mathematical terms, minimizes the oo-norm of the sensitivity function weighted by fE(jtj). 

For the //oo-control problem, from equation (9.131), the oo-norm of the weighted sensitivity funetion ean be written... 

Overall, EGR and combustion/injection systems constitute the key factors to comply with the EuroIV standards (applied in January, 2005). The EuroIV step exhibits EuroIII NO and soot particles limits divided by 2. Besides, vehicle s weight is always increasing due to the introduction of new safety systems and equipment. Therefore, pollutants emissions increase and a supplementary effort to reach the normative threshold is to be made. To comply with this target, some evolutions have been introduced, as for example multi-injection or water-cooling of the EGR system. The NO,/particle compromise adjustment remains possible for most of the applications without any after-treatment system like the Diesel particle filter (DPF). 

Table 5.16. Major-element composition (weight percent) of a komatiitic liquid and normative minerals.

In this brief survey on molecular weights of polymers emphasis has been laid on abnormal behaviour and difficulties, which do not of course constitute the norm. 

As a norm, polyester molecular weights are reported by their intrinsic viscosities (IV), [r ]. The two are related by the Mark-Houwink equation, as follows ... 

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