Applying Lagrange's formula with the observation that Ω • r ( t ) = 0 at all times,

Applying higher pressure of the order of hundreds or thousands of kilobars induces a series of phase transformations, in particular with a tetragonal phase appearing at about 900 kbar.

Applying Chow's analysis to the case of the unexpected hanging ( again with the week shortened to two days for simplicity ), we start with the observation that the judge's announcement seems to affirm three things:

Applying a conception of such illocutionary acts according to which they are ( roughly ) acts of saying something with the intention of communicating with an audience, he describes indirect speech acts as follows: " In indirect speech acts the speaker communicates to the hearer more than he actually says by way of relying on their mutually shared background information, both linguistic and nonlinguistic, together with the general powers of rationality and inference on the part of the hearer.

Applying the rules and customs of prize law, the courts decided whether the Letter of Marque was valid and current, and whether the captured vessel or its cargo in fact belonged to the enemy ( not always easy, when flying false flags was common practice ), and if so the prize and its cargo were " condemned ", to be sold at auction with the proceeds divided among the privateer's owner and crew.

Applying power to one cathode surrounds it with an orange glow discharge.

Applying a pulse with specified width and voltages to the spades made the sheet advance to the next anode, where it stayed until the next advance pulse.

* Greening The Desert: Applying natural farming techniques in Africa, interview with Masanobu Fukuoka ( retrieved 30 November 2010 )

Applying this recursively gives an algorithm with a multiplicative cost of.

The Cholesky decomposition is commonly used in the Monte Carlo method for simulating systems with multiple correlated variables: The correlation matrix is decomposed, to give the lower-triangular L. Applying this to a vector of uncorrelated samples, u, produces a sample vector Lu with the covariance properties of the system being modeled.

Applying Itō's lemma with f ( S ) =

Applying Itō's lemma with f ( Y ) = log ( Y ) gives

Applying to the French classics the rigorous method used with regard to the texts of the Middle Ages, he published the Pensées of Pascal, revised with the original manuscript ( 1887 – 1889 ), and the Provinciales ( 1891 ), edited with notes.

Applying procedural fairness to an entire society therefore seems certain to create recognizable inefficiencies, and therefore be unfair, and ( by the equivalence of justice with fairness ) unjust.

Applying the rule of description, one occupies oneself with describing instead of explaining.

Applying again Bayes ' theorem, and assuming the classification between spam and ham of the emails containing a given word (" replica ") is a random variable with beta distribution, some programs decide to use a corrected probability:

Applying these methods in the workplace, such as Csikszentmihalyi did with Swedish police officers, can improve morale by fostering a sense of greater happiness and accomplishment, and in correlated to increased performance.

Applying the chaos theory to the second law of thermodynamics, the paradox of irreversibility can be explained in the errors associated with scaling from microstates to macrostates and the degrees of freedom used when making experimental observations.

Applying this algorithm to our problem, and using 10-digit floating-point arithmetic, the solution of greater magnitude, as before, is The other solution is then

Applying this knowledge, Newman's team looked for points on the body where stretching motions did not take place by painting a series of circles over a portion of the body and then watching their deformations as the wearer walked around or performed various tasks.

* Applying fuel directly inside the cup-the cup is then usually put on the skin with the fuel still burning ( the flame will quickly extinguish from want of oxygen ).

Applying a flap technique ( first used by Sir Harold Gillies in 1951 ), the spongiform erectile tissue of the penis is removed, and the skin, with its nerves and vascular system ( blood supply ) still attached, is used to create a vestibule area and labia minora, which then are inverted into the neovaginal cavity created in the pelvic tissue.

Applying the same techniques ( which involved gradual immunization of horses and sheep by administering small doses of venoms, and then extracting, purifying and freeze-drying the antibody portion from the blood of injected animals ), Vital Brazil and his coworkers were able to discover the first sera against two species of scorpions ' ( 1908 ) and spiders ' ( 1925 ) venoms.

The ancient geometers are not done yet, for if the fifth vertex of the pentagon is marked as E and FE and BF are joined ( with FE = BF = z ), then cyclic quadrilateral EFBA will be formed with diagonals length d ( diameter ) and b. Applying the ' Almagest ' theorem yet again:

Applying Bayesian probability in practice involves assessing a prior probability which is then applied to a likelihood function and updated through the use of Bayes ' theorem.

Applying the democratic principle, we can calculate the influence of these two rotations on the satellite by calculating the relative contributions of these two collections of massenergy to the background gravitational field strength at the satellite's location, and then weighting their contributions on the satellite's " sense of rotation " accordingly.

Applying a business model learned from her former boss, Tom McNeill, she began hiring young women and training them in the wild routine, which included such antics as chugging alcohol, setting light to it, then breathing fire.

Morgan filled the fire box with wood again, then started supper and set the table.

She helped him with the dishes, then he brought more water in from the spring before it got dark.

He wiped his lips with a sleeve, then stared at Clayton in a childish kind of wonder.

in the cold dawn the mist swirled low to the ground, then rose with a gust of sudden wind to leave the valley clear.

They poured through the opening in the valley, then spread out in a long line to come at us, brandishing their lances and filling the morning with their spine-chilling scalp cry.

He would pick up the ringing phone with studied negligence, then bark into it with gruff importance.

Then, and only then, with the Jacksons and Dan as their true guests of honor, did the Harrows take time to catch up on the news.

From then on, in keeping with the traditions they had followed since childhood, the whole group settled down to relish their food.

The water in Thor's big swimming pool had been covered with a blanket of thick, foamy soapsuds -- fashioned, of course, from zing -- Joyce had dived from the board into the pool, then swirled and cavorted in her luxurious `` bath '' while cameras rolled.

The finished -- and drastically cut -- product would begin with a hazy longshot of Joyce entering the suds, then bursting above the pool's surface clad in layers of lavender lather, and I had a hunch this item was going to sell tons and tons of soap ; ;

He heard their chattering, and then the sounds of hacking as they dismembered the snake right on the porch with wood axes.

For a brief period each year, the rays of the sun are warm enough to melt some of the snows piled a mile deep at the base of the headwalls, and then the pinnacles glisten in the daytime at high noon, and billions of gallons of water begin their slow seepage under the glaciers and across the rockstrewn hanging valleys on their long, meandering journey to the sea -- running east past the sky-carving massifs of Gurla Mandhata and Kemchenjunga, then turning south and curling down through the jungles of Assam, past the Khasi Hills, and into Bengal, past Sirinjani and Madaripur, until the hard water of the melting snows mingles with the soft drainage of fields and at length fans out to meld with the teeming salt depths of the Bay of Bengal.

A wave of flame rippling through their cave had reached Nagamo, his friend, and with a shriek the man bolted through the entrance, then slowed to the jerky walk of a puppet, his uniform blazing.

at first gratingly, caught by grains of corn -- then with a clash into its slot.

Slug the kid, grab his dough -- at least enough to get to Philadelphia -- and then have a rockin' ball with the doll.

It is well then that in this hour both of `` national peril '' and of `` national opportunity '' we can take counsel with the men who made the nation.

If Franklin was an authentic genius, then Alexander Hamilton, with his exceptional precocity, consuming energy, and high ambition, was a political prodigy.

The useful suggestion of Professor David Hawkins which considers culture as a third stage in biological evolution fits quite beautifully then with our suggestion that science has provided us with a rather successful technique for building protective artificial environments.

This and other fears of the solar system have disappeared gradually, first, with the Ptolemaic system and its built-in concept of periodicity and then, more firmly, with the Newtonian innovation of an universal force that could account quantitatively for both terrestial and celestial motions.