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The above expressions for P([X.sup.[r].sub.n]) are the same as the ones in Corollaries 3.5 and 3.6.
1 (Corollaries 3.73.-9), Theorem 3.3 (Corollary 3.10) and Theorem 3.5 (Corollaries 3.11-3.14), when one of the coefficients [A.sub.ik] (z), i = 1,2, 3,4, is chosen to be identically zero.
Possible corollaries (of negative beliefs): Students fail to recognize their achievements, thus do not actively build upon previous successes such as volitional behaviors (e.g.
The conclusion follows by using the results of Theorems 2 and 3 along with the formulas for the sums of i and of [i.sup.3] (these formulas appeared in the proofs of Corollaries 2 and 5 of Theorem 1).
O'Hara did his best to ignore those impediments; he threatened to bring us closer than we'd imagined possible to th taboo Jerusalem of "feeling." And that is why the spectacle of his insouciance and of all its fond, revolutionary corollaries seems now, more than a decade after the advent of AIDS, and nearly three decades after his death, so irretrievable and utopian.
By using eleven different (but somehow plausible) assumptions, Deardorff proves the following Theorems and corollaries:
To check for underflow, we scale the lower bounds in corollaries 3 and 4 by [omega]/10.sup.10.(R - L) before comparing them to [tau].
Note that [P.sub.0,0] =[[summation].sup.n-1.sub.t-0] n[[S.sub.t,t]] in [G.sub.0] ([H.sub.n] (0, q)) by Corollaries 4.5 and 4.6.
By Theorem 2.1, we can obtain the following corollaries. Consequently, the corresponding results in [4] and [5] are generalized.