Sentence examples for exists a root from inspiring English sources

In the rooted case, there exists a root taxon r such that M ri (P) = 1 for every column i.

Assume that there exists a root q ∈ [2,N] where h q) = 0.

Otherwise, there exists a root (lambda_{4}) satisfying (operatorname{Re}lambda_{4}geq0).

Otherwise, we suppose that there exists a root (lambda_{5}) of (2.9) satisfying (operatorname{Re}lambda_{5}geq0).

A digraph has a directed spanning tree if it has N vertices and (N-1) edges and there exists a root vertex with directed paths to all other vertices and the Laplacian matrix L with a directed spanning tree has the following properties.

Then it follows from Theorem 6.1 that f has only simple zeros in (mathbb{K}) and there exists a root vector ({xiin mathbb{K}^{n}}) of f such that bigglVert frac{x^{(0)} - xi}{d(x^{(0)})} biggrVert _{p} < R. Now Theorem 5.4 implies that the Ehrlich-type iteration (1.18) converges to ξ with order of convergence ({2N + 1}).

If the condition (H21) holds, there exists a positive root (v_{10}>0) of equation (12) such that equation (10) has a pair of purely imaginary roots (pm iomega _{10}=pm isqrt{v_{10}=pm

Then there exists a zero root (a_{0}) such that (f'(a_{0})=0}.

To show the uniqueness of the initial value problem (8) with (9), it suffices to show that there exists a unique root μ ∈ ( 0, 1 a 2 ) of equation (13).

It is found that for large stele-to-cortex permeability ratio, there exists an optimum root length-to-base-radius ratio that minimizes the hydraulic resistance.

Hence, f̃ can be extended as a (C^{1}) iterative root f of F on the whole interval I. Similarly, for each (minmathbb{N}) there exists a continuous iterative root (f_{m}) of (F_{m}), which can be presented by f_{m}(x):= left { textstylebegin{array}{l@{quad}l} tilde{f}_{m} (x), & xin K(F), tilde{F}_{m}^{-1}circtilde{f}_{m} circ F_{m}(x), & xin Ibackslash K(F), end{array}displaystyle right.