Then the largest interval of the existence of any solution X ( t, t 0, X 0, D H 1, g X ( t 0 ) ) of (3.1) for each case is I.
Let { X a,…, X b } be the largest interval of the partition such that (1) for every column with a 1 in r j, one of its possible assignments is in either X0 or X a,…, X b, and (2) for every column with a 0 in r j, some of its possible assignments are outside { X a +1,…, X b −1}.
(i) [ t 0, T ) ( T ≤ ∞ ) is the largest interval of existence of the maximal solution u ( t ) ≡ u ( t, t 0, u 0 ) of the following deterministic fractional differential equation: d u ( t ) = f ( t, u ( t ) ) d t + φ ( t, u ( t ) ) ( d t ) α, u ( t 0 ) = u 0, (8) .
[ t 0, T ) ( T ≤ ∞ ) is the largest interval of existence of the maximal solution u ( t ) ≡ u ( t, t 0, u 0 ) of the following deterministic fractional differential equation: d u ( t ) = f ( t, u ( t ) ) d t + φ ( t, u ( t ) ) ( d t ) α, u ( t 0 ) = u 0, (8).
The highest level of Consumer Surplus is attained under qualitatively similar situations as for the Social Welfare case, with the difference that a (V) merger is cleared for a larger interval of the differentiation ratio.
Also, it has been shown that from time to time the tonal components do not appear in a narrow frequency region but in a large interval of the spectrum.
This is expected given the larger interval of the QTL (28 cM for Rphq3 vs. 4 cM for Rphq2) and Rphq3 may, therefore, account for differential expression of most of the genes with unassigned map positions.
Assume that g ∈ C [ Ω, R ] where Ω is an open set, included ordered pairs ( x, u ) belong to R 2, and ( x 0, u 0 ) ∈ Ω. Suppose that [ x 0, x 0 + η ] is the largest interval of existence of the maximal solution r ( x ) of ( c D a + β u ) ( x ) = g ( x, u ), u 0 ( x ) = u 0. Let [ x 0, x 1 ] be a compact interval of [ x 0, x 0 + η ].
The largest interval of 1067.5 kbp was for the QTL qSSIY3.1, which explained 6.45% of phenotypic variations of SSI for yield (Table 4).
In Figure 5, we continue to examine the effect of large interval on the formation of multi-spikes in (4.1).
A separate paper will be presented for systematic analysis of the agents' behaviors with respect to the large intervals of the parameter settings.
