Sentence examples for an arbitrary path from inspiring English sources

Compared to the FEM, XFEM excels in allowing discontinuities to grow within bulk solids along an arbitrary path.

For an arbitrary path (p=e_1ldots e_n) let i be the minimal integer such that the path (e_{i+1}ldots e_n) is special.

(3) Here (varGamma(boldsymbol {x})) denotes an arbitrary path that connects a point on the boundary to the point x within its interior, and (boldsymbol {z} = nabla_{boldsymbol {x}} u in mathbb{R}^{2}).

Since the only edge c is special it follows that an arbitrary path p of length (ge 1) is special and (l(p)=sd(p).) If the edge e is special then (sd(c^i)=0, sd(c^ie)=1).

As we have mentioned above, (l(p)=sd(p)) for an arbitrary path p. The subset (V_1) is spanned by products (pq^*;) (p,qin Path(Gamma ),) such that (l(p)+l q ge sd(p)+sd q)+deg (pq^*)+1,) but this is an empty set.

To estimate E2-ER binding affinities we note that, since the free energy is a state function, it permits the selection of an arbitrary path connecting the bound and unbound states.

Figure 12 Illustration for the proof of unbounded SF for CSR with Projection Method 1. Theorem 2 implies that 3D-CSR-I may use an arbitrary longer path than the shortest path in the worst case.

Even if voters understood what nominal GDP was - as they currently don't - will they really ever believe that a government is going to withstand years of well above, or well below, target inflation, simply to get back to a particular, fairly arbitrary path for the cash value of the economy that was laid down by the folk who were in power before them?

Its use enables the calculation of the kinetics along an arbitrary cooling path relying solely on a CCT curve.

Using a master equation approach, we follow the time evolution of a system from its equilibrium liquid state through an arbitrary cooling path.

Next, to proceed further, we recall an estimate from [4] (cf. Lemma 3.1 and Theorem 3.1): Suppose (n geq 3) and let ({mathbf{Q}}= {mathbf{Q}}(r)) in (mathscr{C}([a, b]; mathbf{SO}(n))) be an arbitrary twist path.