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The notion of a detecting array (DTA) was proposed, recently, by Colbourn and McClary in their research on software interaction tests. Roughly speaking, testing with a (d, t)-DTA (N , k, v) can locate d interaction faults and detect whether there are more than d interaction faults. In this paper, we establish a general lower bound on sizes of DTAs and explore an equivalence between optimal DTAs and super-simple orthogonal arrays (OAs). Taking advantage of this equivalence, a great number of DTAs are constructed, which are all optimal in the sense of their sizes. In particular, an optimal (2, t)-DTA (N , 5, v) of strength t = 2 or 3 is shown to exist whenever v ≥ 3 excepting (t, v) ∈ {(2, 3), (2, 6), (3, 4), (3, 6)}.

The eigenvalues and eigenfunctions of the Schrödinger equation with a Pöschl–Teller (PT)-like potential are presented. A realization of the creation and annihilation operators for the wave functions is carried out. It is shown that these operators satisfy the commutation relations of an SU(1,1) group. Closed analytical expressions are evaluated for the matrix elements of different functions, sin (ρ) and [Formula: see text] with ρ=πx/L.

A resolvable modified group divisible design (RMGDD) is an MGDD whose blocks can be partitioned into parallel classes. In this article, we investigate the existence of RMGDDs with block size three and show that the necessary conditions are also sufficient with two exceptions. #