Sentence examples for term there exists from inspiring English sources

Corollary 4.12: For any p(x) binary polynomial with a constant term, there exists an exponent t, such that p(x) | x t + 1 mod 2. Proof: Write the polynomial p(x) (not divisible by x) as a product of powers of irreducible factors.

In modern terms, there exists a positive line bundle L on X, with Chern class (A in H^2 (X, {mathbb {Z}}) = H^2 (Lambda, {mathbb {Z}}) = wedge ^2 ({{mathrm{text {Hom}}}}(Lambda, {mathbb {Z}}))), whose curvature form, equal to H, is positive (the existence of a positive line bundle on a compact complex manifold X implies that X is projective algebraic, by Kodaira's theorem, [247]).

In more general terms, there exists a deep gap between the education and halakhic identity of the Shas cadres, and the cultural ideal they seek to represent.

Clearly, if the term is x or xx, that is of length 1 or 2, then there is only one way to form a term, that is, there exists just one possible term in each case.

(ii') if a sequence {x n } converging to some u ∈ X has every two adjacent terms comparable, then there exists a subsequence x n k having each term comparable with x.

(i′) if a sequence { x n } converging to some u ∈ X has every two adjacent terms comparable, then there exists a subsequence { x n k } having each term comparable with x.

In other words, in terms of evolution, there exists correspondence between TFs and their TFBSs.

In the PDE literature, one typically needs uniform non-degeneracy of G ε in terms of γ, namely there exists a constant c 0>0 such that begin{array}rcl@ G_{varepsilon}left(cdot, gamma + gamma^{prime}right) - G_{varepsilon}(cdot, gamma) ge c_{0} text{tr}left(gamma^{prime}right),quad forall gamma, gamma^{prime}in mathbb{S}^{d} ~text{with}~gamma^{prime} ge textbf{0}.

Under some super-linear conditions on the non-linear term f, they proved that there exists λ ∗ > 0 such that (1.1) has one positive solution for 0 < λ < λ ∗.

While short-term predictability within time spans of 10 20 ms and AR modeling of the signal have been used effectively [12, 13], there exists a longer-term predictability due to inertia of human vocal organs and their neural control mechanisms.

At present, there exists a lack of long-term outcome data about the impact of SCPs.