Sentence examples for exists a proper from inspiring English sources

There exists a proper bias to give rise to a small surface roughness.

We show that there exists a proper σ-weakly closed subalgebra of N⋊θR which contains N⋊θR+ and is not an analytic crossed product.

From the Poincaré inequality, there exists a proper constant λ 1 > 0, such that λ 1 ∥ u ∥ 2 ⩽ ∥ u ∥ 1 2, ∀ u ∈ V. (2.9).

The first example of such an application is of course the classical result of Fatou and Bieberbach which states that there exists a proper subdomain of which is biholomorphic to.

where r ≠ 0 is a parameter, f : ℝ → ℝ is continuous, m(t) ≠ 0 for t ∈ T and m : T → ℝ changes its sign, i.e., there exists a proper subset T + of T, such that m(t) > 0 for t ∈ T + and m(t) < 0 for t ∈ T T +.

Then either f has form (2.2) for all x ∈ ( 0, + ∞ ) or there exists a proper subinterval I (open or closed or closed on one side; possible infinite or degenerated to a single point) of the half-line ( 0, + ∞ ) satisfying γ x α ∈ I for all  x ∈ I (2.3).

Scherer and Zentner also noticed that in some languages such as English or French there does not exist a proper noun denominating the state of being moved, while it would correspond to the concepts of Rührung or Ergriffenheit in German.

A matrix A is called reducible if there exists a nonempty proper subset (Isubset N) such that (a_{ij}=0), (forall i in I), (forall jnotin I).

Definition 1.2 The tensor A is called reducible if there exists a nonempty proper index subset J ⊂ { 1, 2, …, n } such that a i 1, i 2, …, i m = 0, ∀ i 1 ∈ J, ∀ i 2, …, i m ∉ J.

Definition 1.1 The tensor is called reducible if there exists a nonempty proper index subset J ⊂ { 1, 2, …, n } such that a i 1, i 2, …, i m = 0, ∀ i 1 ∈ J, ∀ i 2, …, i m ∉ J.

(mathcal{A}) is called reducible if there exists a nonempty proper index subset (mathbb{J}subset N) such that a_{i_{1}i_{2}cdots i_{m}}=0, quad forall i_{1}inmathbb{J}, forall i_{2},ldots,i_{m}notinmathbb{J}.