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By Hongquan Xu

A typical challenge that experimenters face is the alternative of fractional factorial designs. minimal aberration designs are familiar in perform. There are occasions within which different designs meet sensible wishes greater. a list of designs could aid experimenters decide upon the easiest layout. according to coding conception, new tools are proposed to categorise and rank fractional factorial designs successfully. we've got thoroughly enumerated all 27 and 81-run designs, 243-run designs of answer IV or better, and 729-run designs of answer V or larger. a set of important fractional factorial designs with 27, eighty one, 243 and 729 runs is given. This extends the paintings of Chen, sunlight and Wu (1993), who gave a suite of fractional factorial designs with sixteen, 27, 32 and sixty four runs.

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The idea was current of the cry, for instance, as the natural ' expression ' of feeling in the sense of that which gave vent to feeling, its natural outlet, and which later could be chosen as a sign. But the idea of an expression in the strong sense, which also defines what the feeling is, only arises with the new theory of man. Language describes the world, but it also has to realize man and through this clarify what he is. It was in this respect that it was continuous with art, at least with the new understanding of art which was developed by the generation of the Sturm und Drang.

So they not only describe a world, they also express a mode of conscious­ ness, in the double sense outlined above, that is, they realize it, and they make determinate what mode it is. This is one of Herder's great seminal ideas. If man is a being who is to be understood under the category of expression, if what is characteristic of him is a certain form of consciousness, Besonnenheit, and if this is only realized in speech, then thought, reflection, the distinctively human activity is not some­ thing which can be carried on in a disembodied element.

For the young Friedrich Schlegel the task was to unite Goethe and Fichte, the former's poetry representing the highest in beauty and harmony, the latter's philosophy being the fullest statement of the freedom and sublim­ ity of the self. To unite the two, as Schlegel for a time thought he saw them united in Wilhelm Meister, would bring men to a new height of consciousness and art. Where the French had revolutionized the political world, the Ger­ mans inaugurate a new, higher cultural era. Others, such as Schleiermacher and Schelling, talked of uniting Kant and Spinoza, the latter being transposed as mentioned above into life-categories and as such a paradigm of that unity of the subject with the All demanded by expression theory.

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A catalogue of three-level regular fractional factorial designs by Hongquan Xu


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