Sentence examples similar to valid for all from inspiring English sources

The cards, valid for all 15 restaurants, will be sold on the lower level.

Then the following statements are valid for all (tauin[0,tau^{0})).

By I we denote points where (I) is valid for all (r>0) and by RI we denote points where (RI) is valid for all (r>0).

(4.3) Moreover, the integral representation (2.28) is valid for all (0<theta<1).

The double inequality frac{8text331}{10text000}log biggl(1+frac{1}{u} biggr)< e^{u}Ei u)< log biggl(1+frac{1}{u} biggr) is <span class="lh">valid for all (u>0).

If (ageq2) and (bleq a_{0}), then inequality (3.16) is valid for all (p>1) and (x>0) follows easily from (1.3) and Lemma 2.5.

In particular, if s is an integral function such that (s' neq0), the extension is valid for all (rho<1) except for (rho=0).

Using a Euler expansion on the above Mercator series gives another Mercator series as log x x − 1 = 1 x + 1 2 x 2 + 1 3 x 3 …, which is valid for all x>1.

Elezović, Giordano and Pečarić [17] established the double inequality biggl(frac{1}{2}+sqrt{frac{1}{4}+x} biggr)^{1-x}x^{x}< Gamma (x+1)< 2^{1-x}x^{x} (1.2) for the gamma function being <span class="lh">valid for all (xin 0, 1)), and asked for 'other bounds for the gamma function in terms of elementary functions'.

Zhu [7] proved that the inequalities (1-lambda) biggl(frac{x}{sin x} biggr)^{p}+lambda biggl( frac {x}{tan x} biggr)^{p}< 1< (1-eta) biggl(frac{x}{sin x} biggr)^{p}+eta biggl(frac {x}{tan x} biggr)^{p} are valid for all (xin 0, pi/2)) if ((p, lambda, eta)in{ p, lambda, eta)| pgeq1, lambdageq1-(2/pi)^{p}, etaleq1/3} cup{ p, lambda, eta)| 0leq plambdageq1/3dageta/3, eta leq 1-(2/pi)^{p}}).

Hence, the previously held association of B2 as a whole with urosepsis may be an oversimplification due to the strong contribution of CC1 and CC4 to isolates of this group, and may thus not be valid for all B2 strains.