Sentence examples for which existed by from inspiring English sources

By this stage of the insurgency, the MNLA had largely split into small groups of guerrillas, which existed by basing themselves in a chosen rural area, subverting local villagers and accumulating from them manpower and supplies.

Let which exists by strong minihedrality.

Open image in new window, which exists by Definition 5 and Lemma 1 6).

Let v 2 be a measurable selection for U (which exists by Kuratowski-Ryll-Nardzewski's selection theorem [21, 22]).

which exists, by standard arguments, since the above problem is just (8a - 8b) with m = − a ( ℓ, u ¯, ⋅ ) − b ( ⋅, p ).

We must distinguish between the nature of God and the nature of things, between that which exists by itself (God) and that which exist by another (the universe), but since the nature of God just is Being itself, no parallel distinction may be drawn between the being of God and the being of things.

From Theorem 2 there exist a minimal nonempty, weakly compact, and convex T-invariant subset E of C and (alpha>0) such that for each a.s.p. sequence ((z_{n} )) in E limsup_{nrightarrowinfty} Vert z_{n} - z Vert geqalpha, quad z in E. Consider an a.s.p. sequence ((x_{n})) in E, which exists by hypothesis.

Remark 2.8 If we denote by H + inv the limit of H k − 1 as k → ∞, which exists by (2.8), then the formulas in (2.11) for the center and matrix radius of the limiting Weyl disk reduce to P + = − J + i δ H + inv , R + = [ H + inv ] 1 / 2. (2.12..

Unfortunately, if the proposition expressed by the condition $\forall q(Qq\rightarrow \neg q)$, which exists by (B), is the only proposition that is Queried, then it is true if and only if it is false, and a contradiction ensues.[15] Propositional quantification made an early appearance in Lewis, Langford, & Lamprecht 1932, which is commonly acknowledged to have pioneered the study of modal logic.

But in order to get there I need to have a proper piece of music, like a symphony, with all the themes, which exists by itself.

This symbol is not a recognizable form of anything that is already finished, already made, or already existent in the world – it is a symbol of a new world, which is being built upon and which exists by the way of the people".