It is obvious that the careful choice of photocathode which maximizes Af for a given input E ( in the case of the second stage, for the first phosphor screen emission ) is very important.

`` One shouldn't mix commercial affairs with patriarchy, but in this case I have no choice.

In many cases such a selection can be made without invoking the axiom of choice ; this is in particular the case if the number of bins is finite, or if a selection rule is available: a distinguishing property that happens to hold for exactly one object in each bin.

However, that particular case is a theorem of Zermelo – Fraenkel set theory without the axiom of choice ( ZF ); it is easily proved by mathematical induction.

In the even simpler case of a collection of one set, a choice function just corresponds to an element, so this instance of the axiom of choice says that every nonempty set has an element ; this holds trivially.

In the case of the complex numbers, C, there is a unique nontrivial automorphism that sends R into R: complex conjugation, but there are infinitely ( uncountably ) many " wild " automorphisms ( assuming the axiom of choice ).

In this case, is the smallest σ-algebra that contains the open intervals of R. While there are many Borel measures μ, the choice of Borel measure which assigns for every interval is sometimes called " the " Borel measure on R. In practice, even " the " Borel measure is not the most useful measure defined on the σ-algebra of Borel sets ; indeed, the Lebesgue measure is an extension of " the " Borel measure which possesses the crucial property that it is a complete measure ( unlike the Borel measure ).

In any case, Gallus had no choice but to get rid of the Goths as soon as possible.

If the axiom of choice is assumed, as will be the case in the rest of this article, then the two definitions are equivalent.

In any case, warfare in the Middle Ages tended to be dominated by raids and sieges rather than pitched battles, and mounted men-at-arms rarely had any choice other than dismounting when faced with the prospect of assaulting a fortified position.

In each case, the differences lie in the choice of the income stream and discount rate.

In other words, he made the correct choice ( in this case predicting an outcome ) for the wrong reasons.

This puts the burden of choice on the individual Muslim, who, in case of conflict, will be forced to decide whose opinion is more likely to be correct.

* Efforts to improve fairness by reducing first-move advantage include the rule of swap, generalizable as " swap -( x, y, z )" and characterizable as a partially compounded and partially iterated version of the pie rule (" one person slices ; the other chooses "): One player places on the board x stones of the first-moving color and a lesser number y stones of the second-moving color (" slicing " in the pie metaphor ); the other player is entitled to choose between a ) playing from the starting position, in which case the selecting player is also entitled to choose which color to play, and b ) placing z ( usually-y ) + 1 ) more stones on the board at locations of that player's choice (" reslicing " in the pie metaphor, with limitations created by the board's existing setup akin to limitations arising from the existing slices in the pie ), in which case the former player is entitled to choose which color side to play.

In many case removal of the offending process gave one the choice to save one's data and exit running programs before rebooting the system.

The state variable S may be a 32-or 64-bit unsigned integer ; in that case, S0 can be 0, and G ( S, n ) can be just S mod n. The best choice of F is a complex issue and depends on the nature of the data.

The extension ψ is in general not uniquely specified by φ, and the proof gives no explicit method as to how to find ψ: in the case of an infinite dimensional space V, it depends on Zorn's lemma, one formulation of the axiom of choice.

If the case has been submitted to arbitration rather than a national court, say because of a forum selection clause, an arbitrator may decide not to apply local mandatory policies in the face of a choice of law by the parties if this would defeat their commercial objectives.

Mr. Pitt's case in ' 84 is the nearest analogy ; but then the people only confirmed the Sovereign's choice ; here every Conservative candidate professed himself in plain words to be Sir Robert Peel's man, and on that ground was elected.

Still made today, they remain a popular choice even for home use since they fold up to the size of a brief case and thus are easy to store.

In Sobhuza II's case, his grandmother theNdlovukati Labotsibeni Mdluli was regent from his choice as infant heir in 1899 following the death of his father Bhunu until his accession to full authority in 1922, when his mother Lomawa Ndwandwe became the ndlovukati.

Since wordplay is often unique to the language in question, translators are faced with a choice of either staying faithful to the original — in this case the English adjective and virtue earnest — or creating a similar pun in their own language.

An obvious choice for this fraction is ½ (− 3 dB ), in which case the diameter obtained is the full width of the beam at half its maximum intensity ( FWHM ).

In any case, he had no intention of being caught asleep, so he carried his revolver in its holster on his hip and he took his Winchester with him and leaned it against the fence.

Curt's visit to the livery stable had been merely a precaution in case anyone should be watching.

The pretty little twittering WACS said he had the look of eagles -- and Penny, hating the cliche, had to admit that in this case it applied.

In this case others should not have had to raise the doubts and fears.

Gross had received Marshall courteously and they were discussing the case.

`` The case was that Bang-Jensen came up to Shann claiming he had found further errors in the report.

New Orleans had a notorious red-light district extending over twenty-eight city blocks, and the business-minded mayor of the city journeyed to Washington to present the case for `` the God-given right of men to be men ''.

yes, they had read about the case ; ;

She and her husband had formerly lived in New York, where she had many friends, but Mr. Flannagan thought the country would be safer in case of war.

Without comment he opened the closet and from its shelves constructed a highboard around the egg case which he had placed on the floor inside.

He had on his gray tweed overcoat and his city hat, and his brief case lay on the bench.

No previous antitrust case, he said, had involved interests of such magnitude or presented such complex problems of relief.

But if true, it was the case of which he had dreamed, the case which would throw him into headlines all over America as the hero of a great murder trial.

I fought like a tigress but by the time I appealed my case to the Supreme Court ( 1937 ), Mr. Roosevelt and his `` henchmen '' had done their `` dirty work '' all too well, even going so far as to attempt to `` pack '' the highest tribunal in the land in order to defeat little me.

How in the world had he formerly found time to build up a business, raise a family, be on half a dozen boards, work actively on committees and either go out in the evening or plow through the contents of a bulging brief case??

She clearly agreed that this had been the case.

But it is crucial that here, unlike Burford, the trial court was ordered to retain the case until the state courts had had a reasonable opportunity to settle the state-law question.

That is, he did not claim in any of the four courts through which his case progressed that the jury charge had denied him any federal right.

If anyone asked us, after we made the remark that the suffering was a bad thing, whether we should think it relevant to what we said to learn that the incident had never occurred and no pain had been suffered at all, we should say that it made all the difference in the world, that what we were asserting to be bad was precisely the suffering we thought had occurred back there, that if this had not occurred, there was nothing left to be bad, and that our assertion was in that case mistaken.