Note on the Phosphorescence of Uranyl Salts (1916)(en)(6s) by Nichols E. L.

By Nichols E. L.

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By Nichols E. L.

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Ehrenfeucht, R. Verraedt), 1980. 103. Fixed Point Languages, Equality Languages and Representation of Recursively Enumerable Languages, Journal of the ACM 27, 499–518 (with J. Engelfriet), 1980. 102. Tree Transducers, L Systems and Two-Way Machines, Journal of Computer and System Sciences 20, 150–202 (with J. Engelfriet, G. Slutzki), 1980. 101. Restrictions, Extensions and Variations of NLC Grammars, Information Sciences 20, 217–244 (with D. Janssens), 1980. 100. On the Structure of Node-Label Controlled Graph Languages, Information Sciences 20, 191–216 (with D.

Proof. Let q be the number of equivalence classes of L intersecting D. Let N be the width of L. Let u = u1 · · · un ∈ D∗ , with u1 , . . , un ∈ D. By a general result on congruences, [u1 ] · · · [un ] ⊂ [u] If n > N , then u is the equivalence class of words that are not factors of L. Otherwise, [u] contains at least one of the q + q 2 + · · · q N products of equivalence classes. Thus the number of equivalence classes of L intersecting D∗ is bounded by this number. The proposition is false if the width is unbounded.

Vn ∈ D. There exists a unique word X1 · · · Xn ∈ V ∗ such that ∗ ∗ S −→ gX1 · · · Xn d for some words g, d and some axiom S, and Xi −→ vi . We denote this word X1 · · · Xn by X(u). Define an equivalence relation on words in D∗ by u ∼ v if and only if X(u) ≡RX,a X(v) for all X ∈ V and a ∈ A. Here ≡RX,a is the syntactic congruence of the language RX,a . Since the sets RX,a are regular, there are only finitely many equivalence class for ∼. We show that u ∼ v implies u ≡L v. This shows that the set of Dyck words that are factors of words in L are contained in a finite number of classes for ≡L .

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