Sentence examples for exists a square from inspiring English sources

(iii) There exists a square integrable function (zeta _{F}:[0,b]rightarrow[0,infty)) such that, for each bounded (Dsubset mathcal{B}), chibigl(F t,D bigr)leq zeta_{F}(t)sup_{-infty< thetaleq0} chibigl(D theta bigr) for a.e.

Two positive systems ( A, B ) and ( A ˆ, B ˆ ) are positively similar if there exists a square nonnegative monomial matrix M satisfying A ˆ = M − 1 A M and B ˆ = M − 1 B. In [14] it is established that the positive reachability property is transferred under positive similarity.

There exists a square integrable function (zeta _{F}:[0,b]rightarrow[0,infty)) such that, for each bounded (Dsubset mathcal{B}), chibigl(F t,D bigr)leq zeta_{F}(t)sup_{-infty< thetaleq0} chibigl(D theta bigr) for a.e. (t in[0,b]), where (D theta)={u(theta):uin D}).

If there exists a square r × r submatrix of D (q ) whose determinantal degree is ∑ k i, the matrix is said to be row reduced.

For each pair of overlapping squares, the second half of the first square is the first half of the second square; so it suffices to check whether there exists a square at position i+ p with the same period.

By making use of the Smith canonical form, there exists a square non-unimodular E (q ) with E (0 ) nonsingular and a matrix D ¯ 2 (q ) with full rank for all q such that L 2 (q ) = E (q ) D ¯ 2 (q ) and the matrix D ¯ 2 (q ) can be assumed to be row reduced without loss of generality.

Let (U=Omega _S eta )setminus ]-infty, 0].) Then U is a simply connected slitted disk on which exists a holomorphic square root q of z.

Moreover, for any cartesian (c c_1 rightarrow c) and vertical (v c_2 rightarrow c), there exists a cartesian square Open image in new window (4.19 in (mathcal {C}) with cartesian (c') and vertical (v').

(A2) The function f satisfies the following Lipschitz condition: there exists a nonnegative constant square matrix K of order 2 such that ∀ t ∈ [ 0, T ] ∀ u, v ∈ D : | f ( t, u ) - f ( t, v ) | ≤ K | u - v |. (A3) The subset D γ : = { z = col ( 0, z 2 ) ∈ D : B ( z, γ ( z, λ ) ) ⊂ D for all  λ ∈ Λ }. is non-empty, where B z, γ z, λ)) := {u ∈ ℝ2 : |u - z| ≤ γ z, λ)}.

For the sake of simplicity, we assume that there exists a non-negative constant square matrix K of dimension n such that | f ( t, x 1 ) − f ( t, x 2 ) | ≤ K | x 1 − x 2 | (1.5).

A converse is also true in the sense that, for a non-negative operator A, there exists a unique non-negative square root B such that A = B^2=B^ B.\, In a sense made precise by the spectral theorem, self-adjoint operators can usefully be thought of as operators that are "real".