Sentence examples for extension of the map from inspiring English sources

The isomorphism is the (Bbbk )-linear extension of the map (delta _{x_1x_2cdots x_n}mapsto x_1otimes x_2otimes cdots otimes x_notimes varepsilon ) for (x_iin X).

Define linear maps (R_k:mathbb {F}_p^{X^{n+1}}longrightarrow mathbb {F}_p^{X^n}), (k=0, 1, ldots, p-1), as the linear extension of the map begin{aligned} b_{i_1}otimes cdots b_{i_n}otimes b_{i_{n+1}}mapsto langle b_k'|b_{i_{n+1}}rangle cdot b_{i_1}otimes cdots b_{i_n}.

In the boundary condition, (frac{partial u}{partial n_{a}}) denotes the conormal derivative of u and is defined by extension of the map C^{1} overline{Omega})ni ulongmapsto bigl(a(Du),n bigr)_{mathbb{R}^{N}} to all (uin W^{1,p}(Omega)), with n being the outward unit normal on ∂Ω.

Here we have focused on hard partitions and the flow of random walkers, but in a subsequent paper we will demonstrate the natural extension of the map equation to overlapping partitions and generalized flows.

If the region mapped contains large duplicated sequence elements, this chromosome walking could potentially lead to the extension of the map into unlinked chromosomal regions.

Advective diffusive transport in microflows is studied by means of the diffusive mapping method, a recent extension of the mapping method by Gorodetskyi et al. (2012. Phys. Fluids 24) that includes molecular diffusion.

The most apparent difference between both representations is the spatial extension of the maps and the more complicated structure of the visual wulst map (see below).

In the present study, we have performed a haplotype-assisted extension of the mapping design and thus increased the allele frequency of the minor QTL allele in mapping families.

The direction model can be considered an extension of the direction map because it captures more than one motion modality at each of the scene's spatial locations.

GEM-TREND can be considered as an extension of the Connectivity Map and a supplementary tool of GEO.

Since the extension of the RH map (see later), seven additional BAC clones were obtained by screening the library with 17 other GGA25 markers (Table 1).