Sentence examples for mappings are shown from inspiring English sources

Figure 2 The frequency to channel assignments for the Smt-LF (filled circles), Smt-MF (filled squares) and Std (open circles) mappings are shown here together with the Greenwood function (dashed line, secondary y -axis).

The TEM images and oxygen and tungsten mappings are shown in Figure 2. Nanorods with diameters of about 10 to 20 nm and various lengths were confirmed in the TEM image in Figure 2a.

Examples of these mappings are shown in Table 3.

The resulting mappings are shown in Figure 4G–I.

T : H → H is said to be strongly nonexpansive [22] if T is nonexpansive and if, for bounded sequences { x n }, { y n } ⊂ H, ∥ x n − y n ∥ − ∥ T x n − T y n ∥ → 0 implies ∥ x n − y n − ( T x n − T y n ) ∥ → 0. The following properties for strongly nonexpansive mappings were shown in [22]: Fix ( T ) is closed and convex when T : H → H is strongly nonexpansive because T is also nonexpansive.

The summary statistics of the read mappings is shown in supplementary table S9, Supplementary Material online).

RNAseq reads were aligned to the respective Taphrina genome assemblies using Tophat (v2.0.4 using parameters –mate-std-dev 50 -a 6 -i 10 -I 10000 –min-segment-intron 10 –max-segment-intron 10000; summary of the mappings is shown in supplementary table S9, Supplementary Material online) (Kim et al. 2013), and the mappings were converted into intron hints.

The following classical result for nonexpansive mappings was showed to still hold for α-nonexpansive mappings in a uniformly convex Banach space E. ([2]).

Application of the Simultaneous Localisation and Mapping algorithm are shown using data collected by the vehicle operating on the Great Barrier Reef in Australia.

Mapping statistics are shown in Table S2.

Mapping statistics are shown in Additional file 1.