Factorials second kind

A more fruitful avenue of research may be the search for factorions of the second kind, which are formed by the product of the factorial values for each of their digits. Additionally, hypothetical factorions of the third kind are formed by grouping digits. For example, a factorion of the third kind might have the form... 

The table of results is laid out in a column, and a second column is constructed in which in the hrst four rows the results would be added sequentially in pahs, e. g. Xi + X2, xj, + X4, x + jcg etc., and the lower four rows are calculated by subuacting the second value from dre preceding value thus, JC2 — JCi, JC4 — JC3 etc., a thh d column is prepared from these results by canying out the same sequence of operations. The process is continued until there are as many columns as the number of variables. Thus in the present tluee-variable, two level-study the process is repeated tluee times (Table 15.1), and in the general -variable, two-level case it is repeated n times. (The general description of uials of this kind where tlrere are n variables and two levels, is 2 factorial uials ). 

An indication of the kinds of improvisations both tolerated and required may be inferred from an astute case study of two East German factories before the Wall came down in 1989. Each factory was under great pressure to meet production quotas—on which their all-important bonuses depended—in spite of old machinery, inferior raw materials, and a lack of spare parts. Under these draconian conditions, two employees were indispensable to the firm, despite their modest place in the official hierarchy. One was the jack-of-all-trades who improvised short-term solutions to keep machinery running, to correct or disguise production flaws, and to make raw materials stretch further. The second was a wheeler-dealer who located and bought or bartered for spare parts, machinery, and raw material that could not be obtained through official channels in time. To facilitate the wheeler-dealer s... 

This happens in two kinds of circumstances. The first may be involuntary, when the experiments are carried out sequentially, in two or several stages. This may be for reasons of economy, when a preliminary fractional factorial experiment has been carried out and a complementary design added some time later, to clarify the ambiguities in estimations of the main and interaction effects. The extrusion-spheronization experiment where a 2 design was followed by a second 2 foldover design is an example of this. 

Unlike the layered systems, the wet lay-up systems are shaped into a composite onsite and due to their ease of application are more widely used. They typically come in two different types. The first type involves some type of fabric or sheet made of usual fibres (including carbon fibres, glass fibres and aramid fibres), impregnated by in situ application of resin to the materials. The second variations of the wet lay-up systems are cloths preimpregnated in the factory which are activated by heat, water or other catalysts in the field. These kinds of systems are normally protected in sealed bags and cold environments because once the bag is opened, the chemical reaction between the material and moisture in the environment temperature begins and the product wUl start curing. 

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