Then the pullback of the covector determined by g ( denoted dg ) is given by

Then the joint distribution of X and Y is completely determined by our channel and by our choice of, the marginal distribution of messages we choose to send over the channel.

Then, if guilt is determined, they decide the appropriate penalty.

Then, after putting the matter to God in prayer, he determined that the first person to enter his room the next morning should be the next Emperor, and that person was Justin, the chief of his guards.

Then, in 1846, the element ilmenium was claimed to have been discovered, but later was determined to be impure niobium.

Then we imagine the rays are parallel ( and given by two angles ), and we let the colour of a point on the surface be determined by the angle between this direction and the slope of the surface at the point.

Then, by projecting the muzzle on the screen with the measured angles the impact point is determined.

Then Y is completely determined by X, so that X and Y are perfectly dependent, but their correlation is zero ; they are uncorrelated.

Then the set of rational points on C may be determined as follows:

Then, a tail event is an event whose occurrence or failure is determined by the values of these random variables but which is probabilistically independent of each finite subset of these random variables.

Then, using the formula, the asymptotic behavior can be determined as follows:

Then, if the assembly was composed of Tribes, the order of the vote had to be determined.

Then Yājñavalkya determined not to have any human guru thereafter.

Then, in 1964, thanks to Stanley Dance, Earl Hines ' determined friend and unofficial manager, Hines was " suddenly rediscovered " following a series of " recitals " at The Little Theatre in New York that Dance had cajoled him into.

The frame bundle F ( E ) can be given a natural topology and bundle structure determined by that of E. Let ( U < sub > i </ sub >, φ < sub > i </ sub >) be a local trivialization of E. Then for each x ∈ U < sub > i </ sub > one has a linear isomorphism φ < sub > i, x </ sub >: E < sub > x </ sub > → R < sup > k </ sup >.

Then a reducible representation of the bonding is determined demonstrated below for water:

Then determined who should be party ’ s declaratory.

Then in 402, he decided to launch an attack on Later Yan itself, determined to protect his Kingdom from further threat.

Then the normal stress and shear stress as a function of the principal stresses can be determined by making.

Then the closed subscheme determined by the base change is the closed image of X ′.< ref > EGA IV < sub > 2 </ sub >, Proposition 2. 3. 2 .</ ref >

Then the flow of net investment per unit of time is determined by balancing losses from having a less-than-optimal level of capital with the adjustment costs of installing new capital ; these adjustment costs in per-unit terms may be an increasing function of the speed of installation.

Then armies and military formations grew, so needed more lodgement area to organize a force large enough to stage a break out against a determined enemy, and again the technical meaning of the term expanded, again referring to a large fortified area about at bridge end.

Then a final vote is taken and the number of delegates for each candidate is determined, proportional to his or her share of the vote.

Then in 2000, Dayton-Hudson renamed itself Target Corporation, having determined that Target was where more of its future growth would be and the more nationally visible division to stockholders.

Then, expecting to be overwhelmed by British reinforcements, they quickly turned back to Fort Erie where they fought a second battle, the Battle of Fort Erie ( 1866 ), against a small but determined detachment of Canadians holding the town.

Then he went back to Britain to kill the British king who wanted to avenge Feng's death, and married the queen of Scotland.

Then Cassivellaunus quarrels with one of his dukes, Androgeus, who sends a letter to Caesar asking him to help avenge the duke's honour.

Then he swears that he would avenge his slain troops and sets out to kill as many demons as possible.

" Then Gilberto dies from his war wound, and as Mungo is just about to avenge the manager's death by killing Chapman, Gaston tackles him to the ground.

Then he calmly and carefully slugged the remaining five shots into the venomous head -- caught in the wicker back of the chair, the eyes dead on him as the life finally went out of the brute.

Then Meltzer's voice, quiet, calm, strong, started the Kaddish, the prayer for the dead.

Then there was a great press to take the king, and such as knew him cried, ' Sir, yield you, or else ye are but dead.

For example, resurrection of the dead, which is exegetically supported by a verse in Exodus 15: " Az Yashir Moshe ..."-" Then will sing ...", from which is derived that " then " ( in the Messianic Era ) Moses will arise and once again sing as he did at the time of the Exodus.

* " Then opened he their understanding, that they might understand the scriptures, And said unto them, Thus it is written, and thus it behooved Christ to suffer, and to rise from the dead the third day: And that repentance and remission of sins should be preached in his name among all nations, beginning at Jerusalem.

Then to his glance appeared the accurst swordbelt surmounting Turnus ' shoulder, shining with its familiar studs — the strap Young Pallas wore when Turnus wounded him and left him dead upon the field ; now Turnus bore that enemy token on his shoulder — enemy still.

Then, on 8 February 1963, a military coup led by a Ba ' athist-Nasserist alliance was staged in Iraq, toppling Qasim who was subsequently shot dead.

Then, on April 11, 1034, Zoe ’ s husband, Romanos III was found dead in his bath.

Then a strange story a few decades later came to start the rumor that the little King John was not dead.

Then I imagined him picking up people in the land of the living and bringing them to the land of the dead, like he's really just a glorified limo or taxi driver.

Then, in February 23, 1942, the Zweigs were found dead of a barbiturate overdose in their house in the city of Petrópolis, holding hands.

Then Trimalchio sets forth his will and gives Habinnas instructions on how to build his monument when he is dead ( 71 ).

Then the dead person's heart was weighed on a pair of scales, against the goddess Ma ' at, who embodied truth and justice.

Then, on April 11, 1034, Romanos III was found dead in his bath, and there was speculation that Zoe and Michael had had him poisoned, then strangled or drowned.

Then it came to the top, dead, and literally boiled.

Then S Silvester put himself to prayer, and S. Peter appeared to him and said: " Go surely to the dragon and the two priests that be with thee take in thy company, and when thou shalt come to him thou shalt say to him in this manner: Our Lord Jesu Christ which was born of the Virgin Mary, crucified, buried and arose, and now sitteth on the right side of the Father, this is he that shall come to deem and judge the living and the dead, I commend thee Sathanas that thou abide him in this place till he come.

Then remove ' dead ' black stones, replace the white stones with black ones to complete the new generation, and repeat the process.

Then two of the commanders found the back door to the fort and began to attack it, but both were promptly shot dead.

King Arthur's encounter with the giant of St Michael's Mount-or Mont Saint Michel in Brittany-was related by Geoffrey of Monmouth in Historia Regum Britanniae in 1136, and published by Sir Thomas Malory in 1485 in the fifth chapter of the fifth book of Le Morte d ' Arthur: Then came to Arthur an husbandman ... and told him how there was ... a great giant which had slain, murdered and devoured much people of the country ... journeyed to the Mount, discovered the giant roasting dead children, ... and hailed him, saying ... rise and dress thee, thou glutton, for this day shalt thou die of my hand.

10 Then fell she down straightway at his feet, and yielded up the ghost: and the young men came in, and found her dead, and, carrying her forth, buried her by her husband.

* Then on 2 April 1997, The Brittas Empire-Laying the Foundations VHS was released ; it features: ' Laying the Foundations ' ( first episode of series one ), ' Back from the dead ' ( first of series two ), ' Set in Concrete ' ( series two ), ' An Inspector Calls ' ( also series two ) and ' The Trial ' ( first of series three ).

Then he and Ivy were devastated when the two-year old Eleanor died of meningitis, going from healthy to dead in less than 24 hours.

Then the camera pans over all the marine characters introduced during the episode, all of whom are dead.

Then they declared that they had found Marc-Antoine dead, hanged ; since suicide was then considered a heinous crime against oneself, and the dead bodies of suicides were defiled, they had arranged for their son's suicide to look like a murder.