Sentence examples for least dim from inspiring English sources

What Germany wants is to dispel, or at least dim, the dark images of the 20th century and replace them with something lighter, even festive.

Then, the problem (1.3) possesses at least dim M k - 1 distinct pairs of sign-changing solutions.

Thus, there exist at least dim H - - codim H + - 1 = dim { M h ⊕ ⋯ M k } - 1. distinct pairs of sign-changing solutions of problem (1.3).

( I 1 ) there is a constant ρ > 0 such that I | ∂ B ρ ∩ X ≥ 0 ; ( I 2 ) there is a subspace W of E with dim V < dim W < ∞ and there is M > 0 such that max u ∈ W I ( u ) < M ; ( I 3 ) considering M > 0 given by ( I 2 ), I satisfies (PS) c for 0 ≤ c ≤ M. Then I possesses at least dim W − dim V pairs of nontrivial critical points.

If codim H+ = 0, then we consider c j for j ≥ 2. As per the above arguments, J ( 0 ) < c 0 ≤ c 2 ≤ c 3 ≤ ⋯ ≤ c dim H - ≤ c ∞ and if c := c j = ⋯ = c j + l for 2 ≤ j ≤ j + l ≤ dim H- with l ≥ 1, then i(K c ∩ S) ≥ l + 1 ≥ 2. Therefore, J has at least dim H- -1 pairs of sign-changing critical points with values belong to [c0, c∞].

there is a constant ρ > 0 such that I ∂ B ρ ∩ X ≥ 0 ; there is a subspace W of E with dim V < dim W < ∞ and there is M > 0 such that max u ∈ W I ( u ) < M ; considering M > 0 given by (ii), I satisfies ( PS ) c for 0 ≤ c ≤ M. Then I possesses at least dim W − dim V pairs of nontrivial critical points.

He then: "Lusters are least  Dimmed among the damned.

But something's been lost along the way, too, or at least dimmed: a certain tenderness "Girls" had to abandon in order to keep going.

Our food system has been adept at keeping the lights out or at least dimmed.

In other words, there is at least a dim light at the end of a dark tunnel for the Republican Party.

Then problem (1.1) possesses at least k ((dim W_{1}= k<+infty), where (W_{1}subset E )) distinct pairs of nontrivial solutions.