Sentence examples for necessarily planar from inspiring English sources
Also, this distance information can be obtained for arbitrary, not necessarily planar, surfaces.
Unlike trees, rooted phylogenetic networks are not necessarily planar and so the definition of an optimal tanglegram is not immediately obvious for them.
Unlike trees, rooted phylogenetic networks are not necessarily planar and so the definition of a tanglegram is not immediately obvious for them: Let N1 and N2 be two rooted phylogenetic networks on 𝒳1 and 𝒳2, respectively, and let M be a set of connectors between 𝒳1 and 𝒳2.
The technique can be applied to other neuron models, and not necessarily for planar systems; n-dimensional systems would only require an additional computational difficulty in computing the associated ( n − 1 ) ARFs.
Second, the models of lift force are derived for a nominal one-dimensional flow case, i.e., collinear bubble velocity and flow field velocity vectors, but are applied to general three-dimensional simulations where the two velocities are not necessarily co-planar.
The first 'elaborate' representation used a special type for aromatic bonds, the second also added a special type for any aromatic atom, and the third representation used a special notation for planar, not necessarily aromatic, structures.
These unexpected findings were consistent with the notion that the invasive capacity of tumour cells studied in 3D systems is not necessarily correlated with efficient migration on planar 2D surfaces (Torka et al, 2006).
These solutions are valid when several or all species are initially present and, in the case of planar electrodes, when their diffusion coefficients are not necessarily equal.
O. Markish and Y. Leviatan take into account both the thermal and electromagnetic aspects when designing the antenna and suggest that wire antennas such as dipole and bow tie antennas, albeit not necessarily best in terms of gain bandwidth product, are preferable over planar antennas for a typical heating rate requirement [29].
Noncanonical signaling encompasses several different pathways that do not necessarily lead to the activation of β-catenin, of which the best understood is the planar cell polarity (PCP) pathway.
