Sentence examples for order is induced from inspiring English sources

Within grains > 5 μm, long-range anion order is induced within elastically switched domains.

With regard to vector equilibrium problems, most of the existing results correspond to the case when the order is induced by a closed convex cone in a vector space.

If there exists a positive bounded linear operator (B: Xrightarrow X) with (r(B leq1), such that bigl(P+JQN+L_{1}^{-1} I-Q N bigr)xleq Bx, quadtextit{for any } x inpartial Omega_{K}, where this partial order is induced by the cone K in X, then the fixed point index operatorname{ind}_{K} bigl([L,N],Omega_{K} bigr)={1}^{-1} I-Q N

If there exist a constant (C>1) and (u_{0}in Kbackslash {theta}), such that bigl(P+JQN+L_{1}^{-1} I-Q N bigr)xgeq Cx-u_{0}, quadtextit{for any } x in K, where this partial order is induced by the cone K in X, then there exists (R_{0}>0), and for (R>R_{0}), the fixed point index operatorname{ind}_{K} bigl([L,N],B_{R}cap K bigr)={0 }, where (B_{R}={xin X :|x|_{X}< R}).

In fact, otherwise, there exist x 2 ∈ ∂ Ω 2 ∩ K and μ 2 ≥ 0 such that L x 2 − N x 2 = μ 2 e, then we obtain ( L + J − 1 P ) x 2 = ( N + J − 1 P ) x 2 + μ 2 e ≥ 1 ( N + J − 1 P ) x 2, in which the partial order is induced by the cone K 1 in Y. So, x 2 ≥ ( L + J − 1 P ) − 1 ( N + J − 1 P ) x 2 = ( P + J Q N ) x 2 + L 1 − 1 ( I − Q ) N x 2, which is a contradiction to condition (C1).

No scale or ordering is induced.

The added flexibility of this assignment model led to superior energy savings in comparison to earlier approaches. 1 That is, the execution ordering is induced by the loop structure and, hence, it is fixed.

defined on the bounded Ω ⊂ C 1 ( [ 0, T ], E ), where the ordering is induced by the positive cone in R 2 and where mod C denotes the modulus of continuity of a subset Ω ⊂ C ( [ 0, T ], E ).a It was proved in [19] that the function α given by (7) is an m.n.c. in C 1 ( [ 0, T ], E ) that is monotone, non-singular and regular.

defined on the bounded set Ω ⊂ C 1 ( [ 0, T ], E ), where the ordering is induced by the positive cone in R 2 and where mod C denotes the modulus of continuity of a subset Ω ⊂ C ( [ 0, T ], E ).a Such a μ is an m.n.c. in C 1 ( [ 0, T ], E ), as shown in the following lemma (proven in [16]), where the properties of μ will be also discussed.

A comparison of the rheological and SAXS data suggested that changes in the dynamic mechanical response during ordering were induced by the development of individual microstructures acting as physical crosslinks.

Let ((X,leq)) be an ordered Banach space, the partial order '≤' is induced by cone P. (1) A multi-valued operator (T: Xrightarrow2^{X}setminus{phi}) is called increasing, if for (forall x,yin X), (xleq y) implies (T x prec T y)).