(i) satisfies the monotonic condition: for each and each there exists such that, (ii) is compact for each, (iii).
(i) satisfies the following condition; for each and, there exists such that, (ii) is compact for each, (iii).
(ii) for each ; (iii) is a solution of BVP(1.5) if and only if and is a solution of the operator equation in cone ; (iv) is completely continuous.
A map (1.7). is called a measure of noncompactness defined on if it satisfies the following properties: (i) if and only if is precompact, for each, (ii), for each, (iii), for each, (iv), for each.
The SD, σ d decreases with increasing coverage (Fig. 3), and is estimated using the following procedure: (i) regions are binned based on their similarity in log-coverage; (ii) an empirical SD of RLRs, is obtained for each bin; (iii) linear interpolation is used between adjacent bins to make function of d; and (iv) σ d is then estimated by.
(i for each, is closed, (ii)for each, if and, then, (iii)for each sequence in, if, then and as.
(i for each, is a closed set, (ii)for each, if and, then, (iii)for each sequence in, if, then and as.
(i for each, is a closed set, (ii)for each, if and, then, (iii)for each sequence in, if, then as.
(i for each, is continuous, is one to one, and is one to one, (ii)for each, if and, then, (iii)for each sequence in with, and as, (iv) is an u.s.c.s.c
In the IIIDB, users can differentiate access high-confidence and low-confidence predictions of human IIIs (see detailed description in Result section), and then see the full evidence values for each predicted III. Figure 1 shows the IIIDB web interface screen-shots of the III search and isoform module search function in the IIIDB.
The tree generated from this alignment contains separate clades for each RNase III domain subgroup, confirming the characterization of the Mnemiopsis RNase III protein as a Dicer protein.
