Sentence examples for moderately hard problem from inspiring English sources

We demonstrate through a series of empirical tests on real and artificial data that these novel insights into the symmetry of the problem often leads to significant reductions in the gap between the optimal solution and its non-integral linear programming bound relative to the prior art as well as often substantially faster processing of moderately hard problem instances.

We then prove that these constraints can often lead to significant reductions in the gap between the optimal solution and its non-integral linear programming bound relative to the prior art as well as often substantially faster processing of moderately hard problem instances.

USGS hardness (Handa 1964) shows four categories of hardness: soft, slightly hard, moderately hard and very hard.

However, none of the currently serving wells can be classified as such and belongs to either moderately hard or hard category of water hardness.

Table 4 Classification of groundwater samples based on Total hardness (Todd 1980) Hardness (mg/L CaCO3) Water classification 0 75 Soft 75 150 Moderately hard 150 300 Hard >300 Very hard.

Total hardness shows that they range from moderately hard category to very hard category during PRM and POM.

Based on the hardness values, Kolong River water generally falls under moderately hard to hard water category.

The results revealed that ground water is alkaline in nature and total hardness observed in all samples falls under moderately hard to very hard category.

Ausoni spring water samples show total hardness ranging from 144.7 to 499.5 mg/l and classified as moderately hard to very hard water.

The degree of hardness in water is commonly based on the classification: (0 75) soft, (75 150) moderately hard, (150 300) hard, (300) very hard (Todd and Mays 2005).

Riebeckite is a moderately hard mineral with a glassy lustre.