Sentence examples for exists a first from inspiring English sources

and imply that there exists a first integral (415). of the system (4.9) that approaches as ; and there exists a first integral (416). of the system (4.13) that approaches as.

Then either ω ( σ ( t ) ) 1 / 2 n − μ remains negative for all time, or there exists a first time t 0 such that ω ( σ ( t 0 ) ) 1 / 2 n − μ = 0. (3.18).

Among the others who defended Buridan's solution would have been Bonaventure, who, in the course of discussing one of Augustine's arguments for the existence of God (Soliloquies I.15)—i.e., that if no truth exists, then some truth exists; and if some truth exists, a First Truth exists records the objection that the first inference fails because no proposition can entail its own contradictory.

It was proved in [2] that there exists a first curve C of nontrivial Fučík eigenvalues in the sense that, defining η: (λ1, ∞) → ℝ by η def ¯ ¯ inf { μ > λ 1 : is a nontrivial Fu č í k eigenvalue }, we have that λ1< η < ∞ for every λ (>λ1), and the curve C d e f : λ ∈ ( λ 1, ∞ ).

As panel B shows, there exists a first level of genes (FKH1, FKH2, MCM1, SWI6 and CLN3) that are not controlled within the network, and the bottom-most layer (CLB4, APC1, CLB1, CLB2, ACE2, CLN2, CLN1, CLB6, GIN4 and SWE1) represents the terminal nodes of the network, which do not control any other genes in the network.

Thus, by Kronecker existence property of Brouwer degree, there exists a third positive solution.

Mr. Kristof doesn't point out that aside from these two comparatively tiny extremes, there exists a third Israel, which includes the vast majority of its citizens.

A single bookshop in Seattle now exists, a second is on its way, and if rumours are to be believed, every city could soon have one.

As a consequence of the translational quasiperiodicity, there exists a second type of elastic deformation beyond the ordinary sound wave, or phonon.

In Chinatown, there exists a third way of selling fake bags, one that doesn't require false doors or stash houses.

At present, our radar systems are unable to determine if there exists a second disc-shaped object, contained within a new red capsule, which will be delivered to us next, in what the species refers to as a "queue".