Sentence examples for sufficient enlargement from inspiring English sources

The main results of the paper: (1) Each minimal-volume sufficient enlargement is linearly equivalent to a zonotope spanned by multiples of columns of a totally unimodular matrix.

(2) If a finite-dimensional normed linear space has a minimal-volume sufficient enlargement which is not a parallelepiped, then it contains a two-dimensional subspace whose unit ball is linearly equivalent to a regular hexagon.

A symmetric, bounded, closed, convex set A in a finite-dimensional normed linear space X is called a sufficient enlargement for X if, for an arbitrary isometric embedding of X into a Banach space Y, there exists a linear projection P Y→X such that P BY ⊂A.

Sufficient enlargement of the root canal coronal to the fragment is essential for successful retrieval.

In a number of cases, pollination alone (not followed by fertilization) is sufficient stimulus to evoke enlargement of the pistil to form a seedless (parthenocarpic) fruit.

Together, the mouse and chick analyses demonstrate that a Hox4 border is necessary and sufficient to induce apical enlargement.

The dual role of Mfn2 as both mitochondrial fusion factor and Parkin receptor in the mitophagy appears sufficient to explain mitochondrial enlargement, degeneration, and proliferation in Mfn2 deficiency in the heart (Dorn & Kitsis, 2015) and brain (Lee et al, 2012).

As upd overexpression is alone sufficient to drive eye-antennal disc enlargement [25], high levels of extracellular Upd produced by ept cells might be predicted to feed back onto nearby cells (irrespective of their genotype) to elicit the growth and proliferation phenotypes observed in FACS analysis (see Fig. 1).

Finally, it has been reported that bath application of BDNF or forskolin during glutamate uncaging is sufficient to induce protein synthesis dependent spine enlargement (Tanaka et al., 2008; Govindarajan et al., 2011).

This rapid proliferation rate implies that sufficient lipids are available to support both the enlargement of the PVM and membrane neogenesis for newly formed merozoites.

We found that tyrosine mutation in the ITAM of C35, or Syk kinase inhibition, is sufficient to abolish the potential of C35 protein to cause enlargement of acinar structures in 3D cell culture.