Sentence examples for hold sum from inspiring English sources

For any interior point P of the triangle (ABC) and arbitrary non-negative real numbers λ and μ (λ, μ not both zero) the following inequalities hold: sum R_{1}gefrac{2sum(lambda a+mu b+mu c)(r_{1}+R_{1})}{(lambda +2mu sum a}ge2sum r_{1}.

Let k be a real number such that (0le kle2), then for any interior point P of the triangle (ABC) the following inequalities hold: sum R_{1}ge frac{2sum(kh_{a}+h_{b}+h_{c})(r_{1}+R_{1})}{ k+2)sum h_{a}}ge 2sum r_{1}.

Let k be real number such that (0le kle2), then for any interior point P of the triangle (ABC) the following inequalities hold: sum R_{1}gefrac{2sum kR_{1}+r_{2}+R_{3})(r_{1}+R_{1})}{ k+2)sum R_{1}}ge 2sum r_{1}.

For any interior point P of (triangle ABC) and non-negative real numbers λ and μ (λ, μ not both zero), the following inequalities hold: sum R_{1}gefrac{2sum(lambda a+mu b+mu c)(w_{1}+R_{1})}{(lambda +2mu sum a}ge2sum w_{1}.

Let k be a real number such that (0le kle2), then for any interior point P of the triangle (ABC) the following inequalities hold: sum R_{1}gefrac{2sum kR_{1}+R_{2}+R_{3})(w_{1}+R_{1})}{ k+2)sum R_{1}}ge 2sum w_{1}.

But a potent opposition slogan plastered through Monrovia — "Too old to hold" — sums up the counterview of the 72-year-old president: that she has not tackled the country's myriad problems with sufficient energy.

At the end of this paper, he conjectured that the following inequality holds: sum R_{2}R_{3}gesum (r_{3}+r_{1}+r_{2}1}+r_{2}).

(5.2) then for any interior point P of the triangle (ABC) the following inequality holds: sum R_{1}gefrac{2sum k_{1}(r_{1}+R_{1})}{sum k_{1}}.

Once each of the n group founders has obtained an initial share e i of the secret d, to which we'll refer as S G, the following holds: (sum _{i=1}^{n}e_{i}=S_{G}) [57].

If this does not hold, the sum can be weighted according to the penalties incurred for false positives and negatives, i.e. minimise θ × 1-Sensitivity) + (1 - θ )× 1-Sensitivity) where θ is the weight attached to the sensitivity.

Sum theorists believe in the existence of mere sums (defined in 2.2.1) and hold that sums are things.