By Cecil H. Hastings
The description for this publication, Approximations for electronic desktops, might be forthcoming.
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Hence, α(i+1)-th −αi-th in (10) is the interval between the rises of α. (10) shows that the period of the rise of α is 1[s] when the up train is between Shigaraki and Onotani, while (11) indicates the position of the train. β = 13R + 1@B = d (12) This means the down train departs just after (+1 [s]) the time when 13R turns green, where β is a spur for controlling the down train. 0 < j < jmax & j = jmid ⇒ β(j+1)-th − βj -th = 1 (13) (0 < j < jmid ⇒ B = j · v)@βj -th (14) (jmid < j < jmax ⇒ B = d + j · w)@βj -th (15) Let v and w be the speeds of the down train between Kibukawa and Onotani, and between Onotani and Shigaraki, respectively, and jmid and jmax be d/v and d/v + (l − d)/w, respectively.
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For brevity we call them just dg-systems – more about this topic is provided in section 2. The work reported here presents an improvement of theorem reuse in dgsystems in two aspects: 1) the theorem reuse factor is enhanced by embedding into the target theory only the minimal premises of a theorem to be reused instead of the whole set of axioms of the source theory. We call these embeddings partial theory inclusions. 2) Consistent many to many formulae matching is used to detect appropriate signature morphisms for such embeddings.
Approximations for digital computers, by Cecil H. Hastings