If D denotes the differentiation operator and P is the polynomial Af then V is the null space of the operator p (, ), because Af simply says Af.

If Af is the null space of Af, then Theorem 12 says that Af.

`` Before then, my sales during much of the year had lagged behind 1960 by 20% '', he says.

So, I put my Bible to the practical test of noting what it says about itself, and then tested it to see how it worked.

Writing to his colleague George Herbert Palmer -- `` Glorious old Palmer '', as he addresses him -- James says that if only the students at Harvard could really understand Royce, Santayana, Palmer, and himself and see that their varying systems are `` so many religions, ways of fronting life, and worth fighting for '', then Harvard would have a genuine philosophic universe.

He further says that the reason there is no complete conclusive repeatable evidence is because that if the afterlife was so demonstrable then it would become " another chapter in a school textbook " and that " the whole process of questioning, probing, studying, observing, meditating and of wanting so desperately and enduringly to know, is part of the development of mind itself ".

Snorri says at first it is Valhalla and then adds: " The Swedes now believed that he had gone to the old Asagarth and would live there forever " ( Section 9 ).

Mirroring the film further, Peter is then in the same setting in which the much older Salieri was when he says " Go ahead, mock me.

If the sick person wishes to receive the sacrament of penance, it is preferable that the priest make himself available for this during a previous visit ; but if the sick person must confess during the celebration of the sacrament of anointing, this confession replaces the penitential rite A passage of Scripture is read, and the priest may give a brief explanation of the reading, a short litany is said, and the priest lays his hands on the head of the sick person and then says a prayer of thanksgiving over the already blessed oil or, if necessary, blesses the oil himself.

" a Christian ( Minaah ) once asked Abbahu in a tone of mockery, whereupon he replied: " When you will be wrapped in darkness, for it says, ' Behold, darkness shall cover the earth, and gross darkness the nations ; then shall the Lord rise upon thee and His glory shall be seen on thee ' lx. 2 ," ( Sanhedrin 99a ).

She says she has been treated like a doll to play with, first by her father and then by him.

God then rebukes the three friends and says, " I am angry with you ... you have not spoken of me what is right.

According to Tacitus in his Annals, Boudica poisoned herself, though in the Agricola which was written almost twenty years prior he mentions nothing of suicide and attributes the end of the revolt to socordia (" indolence "); Dio says she fell sick and died and then was given a lavish burial ; though this may be a convenient way to remove her from the story.

The city will be taken, the houses looted, and the women raped … Then the Lord will go forth and fight against those nations … Thus the Lord my God will come, and all the saints with you .” 14: 2-5 In Matthew, Jesus says, " The sign of the Son of Man will appear in heaven, and then all the tribes of the earth will mourn, and they will see the Son of Man coming on the clouds of heaven with power and great glory.

It says that if g is a function that is differentiable at a point c ( i. e. the derivative g ′( c ) exists ) and f is a function that is differentiable at g ( c ), then the composite function f ∘ g is differentiable at c, and the derivative is

If a is a point in R < sup > n </ sup >, then the higher dimensional chain rule says that:

Brent says that when in the throes of its pain " he was, at first, almost stupefied, and then aloof, cold, depressed, extremely suspicious, impatient of the slightest crossing, and subject to violent outbursts of temper ".

Columba ’ s other prophecies can be vindictive at times as when he sends a man named Batain off to perform his penance, but then Columba turns to his friends and says Batain will instead return to Scotia and be killed by his enemies.

Second, he does not say that his existence is necessary ; he says that if he thinks, then necessarily he exists ( see the instantiation principle ).

However, because of the Reid v. Covert decision, the U. S. adds a reservation to the text of every treaty that says, in effect, that the U. S. intends to abide by the treaty, but if the treaty is found to be in violation of the Constitution, then the U. S. legally can't abide by the treaty since the U. S. signature would be ultra vires.

Given a left neutral element and for any given then A4 ’ says there exists an such that.

They also point out that in, Paul says that God will reward those who follow the law and then goes on to say that no one follows the law perfectly ( see also Sermon on the Mount: Interpretation )

The well-known historian of physics, C. P. Snow, says about him, " If Fermi had been born a few years earlier, one could well imagine him discovering Rutherford's atomic nucleus, and then developing Bohr's theory of the hydrogen atom.

In this passage Jesus says that an offended Christian should draw the offender's fault to his attention at first privately ; then, if the offender refuses to listen, to bring one or two others, that there may be more than a single witness to the charge ; next, if the offender still refuses to listen, to bring the matter before the church, and if the offender refuses to listen to the church, to treat him as " a Gentile and a tax collector ".

and since then, freedom as a form of political action has been neglected, even though, as she says, freedom is " the raison d ' être of politics.

Chrysippus moved to Athens, where he became the disciple of Cleanthes, who was then the head ( scholarch ) of the Stoic school.

Zeus appeared to her disguised as Artemis, or in some stories Apollo, gained her confidence, then took advantage of her ( or raped her, according to Ovid ).

Denying the immortality of Zeus, then, was the lie of the Cretans.

Zeus then commanded Hermes to kill Argus, which he did by lulling all one hundred eyes to sleep.

Zeus gave her the gift to be able to take her eyes out to rest, and then put them back in.

Zeus swore to give Semele whatever she wanted and was then obliged to follow through when he realized to his horror that her request would lead to her death.

Gaia then took Zeus and hid him deep in a cave beneath the Aegean Mountains.

Zeus then married his third wife Eurynome, who bore the three Charites ( Graces ): Aglaia, Euphrosyne, and Thalia.

"... then Zeus the father created the third generation of mortals, the age of bronze ...

Cronus then placed them back in Tartarus, where they remained, guarded by the female dragon Campe, until freed by Zeus.

Zeus drove Ixion from Mount Olympus and then struck him with a thunderbolt.

Zeus forced Cronus to disgorge the other children in the reverse order in which they had been swallowed, the oldest becoming the last, and youngest: first the stone, which was set down at Pytho under the glens of Parnassus to be a sign to mortal men, then the rest.

She then demanded that Zeus reveal himself in all his glory as proof of his godhood.

Hera then induces Semele to ask Zeus to come to her as a god, she dies, and Zeus seals the unborn baby up in his thigh.

Zeus then ordered Thanatos, god of death, to chain King Sisyphus down below in Tartarus.

37-" The Egyptians, then, having been taught to worship Antinous, will, if you compare him with Apollo or Zeus, endure such a comparison, Antinous being magnified in their estimation through being classed with these deities ; for Celsus is clearly convicted of falsehood when he says, ' that they will not endure his being compared with Apollo or Zeus.

They bring great advantage to those who venerate them ; but if someone dishonors them, then they go to Zeus and ask that Até be sent against that person.

Zeus then led his released brothers and sisters in rebellion against the Titans.

He then said to Zeus " If you think that you are so clever, make your son whole and un-harmed.

Zeus then sent a lightning bolt down and a storm, killing all of Odysseus ' men, while their doom was portended by the meat writhing and lowing on the spits.

She then placed it on the mirrored shield called Aegis and she gave it to Zeus.

She then raised her hands and said a prayer, which was heard by Zeus who took pity on her and turned her into a tree.

In Homer's Iliad, an Oneiros is pictured as summoned by Zeus, receiving from him spoken instructions, and then going to the camp of the Achaeans and entering the tent of Agamemnon to urge him to warfare.