Sentence examples for strictly complete from inspiring English sources

We now apply the condition (i) and Proposition 2.1, the system J i ( S 1, Q ) is strictly complete, and the sets α i and α ¯ i by (3.1) are well defined such that.

The system of matrices {J i }, i = 1, 2,..., N, is said to be strictly complete if for every x ∈ R n {0} there is i ∈ {1, 2,..., N} such that x T J i x < 0. It is easy to see that the system {J i } is strictly complete if and only if ⋃ i = 1 N α i = R n { 0 }, where α i = { x ∈ R n : x T J i x < 0 }, i = 1, 2, …, N. Proposition 2.1.

Definition 2.2 The system of matrices { J i }, i = 1, 2, …, N, is said to be strictly complete if for every x ∈ R n ∖ { 0 } there is i ∈ { 1, 2, …, N } such that x T J i x < 0. It is easy to see that the system { J i } is strictly complete if and only if ⋃ i = 1 N α i = R n ∖ { 0 }, where α i = { x ∈ R n : x T J i x < 0 }, i = 1, 2, …, N. Proposition 2.1 ([38]).

We now apply condition (i) and Proposition 2.1, the system J i is strictly complete, and the sets α i and α ¯ i by (3.1) are well defined such that ⋃ i = 1 N α i = R n ∖ { 0 }, ⋃ i = 1 N α ¯ i = R n ∖ { 0 }, α ¯ i ∩ α ¯ j = ∅, i ≠ j.

We now apply the condition (i) and Proposition 1, the system J i (R, Q) is strictly complete, and the sets α i and α ̄ i by (2) are well defined such that ⋃ i = 1 N α i = R n { 0 }, ⋃ i = 1 N α ̄ i = R n { 0 }, α ̄ i ∩ α ̄ j = ∅, i ≠ j.

We now apply the condition (i), (ii) and Proposition 2.1, the system J i is strictly complete, and the sets α ijl and α ¯ i j l by (3.1) are well defined such that ⋃ i = 1 N α i j l = R n { 0 }, ⋃ i = 1 N α ¯ i j l = R n { 0 }, α ¯ i j l ∩ α ¯ t j l = ∅, i ≠ t.

Formally, also an indefinite exclusive cp-law may be written as a strictly completed law of the form "if disturbing factors are excluded, then As will always be Cs"—only that the meaning of "all disturbing factors" is now unclear and opens the doorway to various sorts of deficiencies, which are discussed in the next section.

When associated strictly with complete nucleus formation and concomitant chain collapse, folding is a well-defined two state event.

Strictly respiring, complete oxidizer that oxidizes acetate with O2, ClO4−, ClO3−, Mn(IV), or NO3− as electron acceptors.

Strictly respiring, complete oxidizer that oxidizes acetate with O2, ClO4−, ClO3−, NO3− or NO2− as electron acceptors.

Theorem 3.3 Let C be a nonempty closed and convex subset of a complete strictly convex hyperbolic space X.