Sentence examples for implies positivity from inspiring English sources

However, the positivity of both x ( t ) and x ( τ ( t ) ) implies positivity of z.

Similarly, analysis of electron energy loss spectra (EELS) also implies positivity on all factors and abundances.

(7) By virtue of (4), the positivity of terms of the sequence ((p_{n})) implies the positivity of terms of the sequence ((b_{n})).

The lower bound implies the positivity of the solution of the Landau equation, and partially answers to an analytical conjecture.

Furthermore, simple inspection of the above equation implies strict positivity.

This implies the positivity of the Green's function of problem (1.1), (1.2).

where we set p 2 i ( s ) = 0 for s < 0, implies the positivity of the Cauchy function of the first order equation (5.3) (see Theorem 15.7, p.358 in [28]).

This in turn implies non-positivity of conventional difference methods.

Proof According to the result of [31], the conditions of Theorem 1 imply the positivity of the Cauchy functions and fundamental solutions of the diagonal equations x i ′ ( t ) − q i ( t ) x i ′ ( g i ( t ) ) + p i i ( t ) x i ( t − τ i i ( t ) ) = f i ( t ), t ∈ [ 0, ∞ ), i = 1, …, n. (18).

However, a significant OR was not obtained among the patients with a transient HBV infection implied by positivity for both antibody to hepatitis B surface antigen and anti-HBc (OR, 1.5; P = 0.48).

Since the class of sequences with the zero boundary conditions on both x 0 and x N + 1 is a subset of the class of sequences with zero boundary condition at 0, the nonnegativity (positivity) of the functional (1) over the class of functions which satisfy x 0 = 0 implies the nonnegativity (positivity) of this functional over the class of functions which satisfy x 0 = 0 = x N + 1.