Linear inverse problems with discrete data: II. Stability and regularization

For pt.I. see ibid. vol.1, p.301 (1985). In the first part of this work a general definition of an inverse problem with discrete data has been given and an analysis in terms of singular systems has been performed. The problem of the numerical stability of the solution, which in that paper was only briefly discussed, is the main topic of this second part. When the condition number of the problem is too large, a small error on the data can produce an extremely large error on the generalised solution, which therefore has no physical meaning. The authors review most of the methods which have been developed for overcoming this difficulty, including numerical filtering, Tikhonov regularisation, iterative methods, the Backus-Gilbert method and so on. Regularisation methods for the stable approximation of generalised solutions obtained through minimisation of suitable seminorms (C-generalised solutions), such as the method of Phillips (1962), are also considered.

Effect of reflow profile and thermal cycle ageing on the intermetallic formation and growth in lead-free soldering

The formation and growth of intermetallic compound layer thickness is one of the important issues in search for reliable electronic and electrical connections. Intermetallic compounds (IMCs) are an essential part of solder joints. At low levels, they have a strengthening effect on the joint; but at higher levels, they tend to make solder joints more brittle. If the solder joint is subjected to long-standing exposure of high temperature, this could result in continuous growth of intermetallic compound layer. The brittle intermetallic compound layer formed in this way is very much prone to fracture and cold therefore lead to mechanical and electrical failure of the joint. Therefore, the primary aim of this study is to investigate the growth of intermetallic compound layer thickness subjected to five different reflow profiles. The study also looks at the effect of three different temperature cycles (with maximum cycle temperature of 25 0C, 40 0C and 60 0C) on intermetallic compound formation and their growth behaviour.. Two different Sn-Ag-Cu solder pastes (namely paste P1 and paste P2) which were different in flux medium, were used for the study. The result showed that the growth of intermetallic compound layer thickness was a function of ageing temperature. It was found that the rate of growth of intermetallic compound layer thickness of paste P1 was higher than paste P2 at the same temperature condition. This behaviour could be related to the differences in flux mediums of solder paste samples used.

Breast milk levels of zinc and omega-6 polyunsaturated fatty acids and growth of healthy Chinese infants

AIM: To examine the concentrations of zinc and omega-6 polyunsaturated fatty acids (omega-6 PUFAs) in breast milk, the impact of zinc on omega-6 PUFA metabolism, and the growth rate of infants. METHODS: Forty-one mother-term infant pairs from a rural area of northern Beijing, China, who were 1 month (n = 18, group I) and 3 months (n = 23, group II) old and exclusively breastfed, were studied. The dietary records and the concentrations of zinc and omega-6 PUFAs in the milk of lactating women and the increase in weight and length of their infants during 1 and 3 postnatal months were analysed. RESULTS: The dietary intakes of mothers in the two groups were the same, i.e. high in carbohydrate and low in fat, protein and energy. The maternal zinc intake was 7.5mg/d and thus reached only 34.6% of the current Recommended Nutrient Intake (RNI). The levels of zinc and arachidonic acid (AA, C20:4 omega-6) in the milk of group I were significantly higher than those in group II. Furthermore, significant positive correlations were found between the concentrations of zinc and AA in the breast milk and between the level of milk AA and weight gain. CONCLUSION: Zinc may be a co-factor and essential for essential fatty acids (EFA) metabolism. Thus suboptimal zinc intake may cause EFA imbalance. Further studies of Chinese rural mother-infant pairs are necessary to determine whether zinc supplementation should be recommended when lactation exceeds 3 months.