hardness

Those needles, they're for... stabilization?

I mentioned NP hardness before.

The hardness of diamond is 10.

Hardness and strength are death's companions.

A vertical takeoff aircraft needs an artificial stabilization system that's essential.

The degree of hardness must be high.

I think I can reconfigure the flight control system for stabilization burn.

One of the qualities of steel is hardness.

It's strength is relies on a hardness of prime factorization.

The hardness of diamond is such that it can cut glass.

Now the furnace has fired you red, your soft hardness yields to the hammer.

like hardness, sharpness, brightness and darkness, and the phonemes that we're able to speak with.

This the beginning of Unit 6, which is going to cover the hardness of network problems.

And if we obey God, we must disobey ourselves and it is in this disobeying ourselves, wherein the hardness of obeying God consists.

So that's kind of cool. So one of the things to point out is that the peak of the hardness comes at K 3.

O you who believe! fight those of the unbelievers who are near to you and let them find in you hardness and know that Allah is with those who guard (against evil).

So as you go through the material, I hope the hardness of the quizzes won't discourage you it'll really entice you to take a piece of paper and a pen and work them out.

There's a whole other set of work that has to go into finding lower bounds on the hardness of problems and that requires very different techniques from the kinds that we've talking about up to this point.

And those properties of softness and hardness and darkness and clearness do not reside in the carbon atoms they reside in the interconnections between the carbon atoms, or at least arise because of the interconnections between the carbon atoms.

So it's worth pointing out what theoreticians often really like to do is that they find an upper bound for the hardness of their problem and they can find a lower bound that matches it, then you know exactly the complexity of the problem.

Thenceforth were your hearts hardened They became like a rock and even worse in hardness. For among rocks there are some from which rivers gush forth others there are which when split asunder send forth water and others which sink for fear of Allah. And Allah is not unmindful of what ye do.

So computational complexity is the problem of actually finding the hardness of problems and from the prospective of a theoretician who studies complexity theory, the stuff that we've been doing so far talking about devising algorithms and proving their running times, that's just part of the story, that's just upper bound determination.

Moses prayed Our Lord! Thou hast indeed bestowed on Pharaoh and his chiefs splendour and wealth in the life of the present, and so, Our Lord, they mislead (men) from Thy Path. Deface, our Lord, the features of their wealth, and send hardness to their hearts, so they will not believe until they see the grievous penalty.

Then, even after that, your hearts were hardened and became as rocks, or worse than rocks, for hardness. For indeed there are rocks from out which rivers gush, and indeed there are rocks which split asunder so that water floweth from them. And indeed there are rocks which fall down for the fear of Allah. Allah is not unaware of what ye do.

Then your hearts hardened thereafter, so they are as stones or stronger in hardness and verily of stones there are some from which gush forth rivers, and verily there are of them some that cleave asunder and water issueth therefrom, and verily there are of them some that fall down in awe of Allah and Allah is not neglectful of that which ye work.

Then, after that, your hearts were hardened and became as stones or even worse in hardness. And indeed, there are stones out of which rivers gush forth, and indeed, there are of them (stones) which split asunder so that water flows from them, and indeed, there are of them (stones) which fall down for fear of Allah. And Allah is not unaware of what you do.

Then your hearts hardened after that, so that they were like rocks, rather worse in hardness and surely there are some rocks from which streams burst forth, and surely there are some of them which split asunder so water issues out of them, and surely there are some of them which fall down for fear of Allah, and Allah is not at all heedless of what you do.