If each node additionally records the size of its subtree ( including itself and its descendants ), then the nodes can be retrieved by index in O ( log n ) time as well.

If both are accepted, one has to additionally signal a preference.

If the aging for one of these types of whiskey reaches two years or beyond, the whiskey is then additionally designated as " straight " e. g., " straight rye whiskey ".

If we use NC reductions, that is, reductions which can operate in polylogarithmic time on a parallel computer with a polynomial number of processors, then all P-complete problems lie outside NC and so cannot be effectively parallelized, under the unproven assumption that NC ≠ P. If we use the weaker log-space reduction, this remains true, but additionally we learn that all P-complete problems lie outside L under the weaker unproven assumption that L ≠ P. In this latter case the set P-complete may be smaller.

If UV / Vis spectrophotometry is used in quantitative chemical analysis then the results are additionally affected by uncertainty sources arising from the nature of the compounds and / or solutions that are measured.

If, additionally, the recipient of the criticism is not the intended target, that is also a factor to consider.

If we additionally assume that the image plane is perpendicular to the ground plane ( an imaginary plane Tangential to the surface of the Earth ), and that the waterfall flows on a plane that is parallel to the image plane, we can estimate the height by measuring the vertical separation of waterfall head and base in

* If the operation additionally has an identity element, we have a commutative monoid

If additionally is injective we say is 1-reducible to and write

If additionally

If, additionally, the real part of s is positive, then the limit γ ( s, u ) → 0 for u → 0 applies, finally arriving at the complex integral definition of γ

If not, then the judge must additionally assess the application under the " centralized mode of existence " approach, guided by the non-exhaustive factors set out in Koo ( Re ).

If the poset P additionally is a join-semilattice ( i. e., if it has binary suprema ) then these conditions are equivalent to the following statement:

If the surface is additionally known to be axisymmetric with,

If a player cannot follow suit, he must play a trump card if able, and additionally, the player is compelled to play a higher trump than any existing trump in the trick if he is able ( The " Petit " or 1 is valued lowest, and the " Monde " or 21 is valued highest ).

If it were a warship, and repairable, usually the Crown bought it at a fair price ; additionally, the Crown added " head money " of 5 pounds per enemy sailor aboard the captured warship.

Their sets included songs spanning Strummer's career to that point, including works from The 101ers and The Clash, additionally material co written with Mick Jones for Big Audio Dynamite's No. 10, Upping St. album as well as a cover of The Pogues ' famous " If I Should Fall From Grace With God.

If the sample is depolarizing the Mueller matrix formalism should be used, because it gives additionally access to the amount of depolarization.

If X was in good faith, and additionally was in legal possession of the house, then any vindicatio brought by Y could be defeated by X using the defence of fraud ( exceptio dolus malus ) until Y paid X for the materials.

If the two vertices are additionally connected by a path of length 1, i. e. by a single edge, the vertices are called adjacent.

If police additionally have reasonable suspicion that a person so detained may be armed, they may " frisk " the person for weapons, but not for contraband like drugs.

If the officer additionally has reasonable suspicion that the person is armed, the officer may perform a search of the person's outer garments for weapons.

If abstract index notation is used also for spinors then these will carry a spinorial index and the Dirac gamma will carry one Lorentzian and two spinorian indices, but it is more common to regard spinors as column matrices and the Dirac gamma as a matrix which additionally carries a Lorentzian index.

If she, Pamela, were being held responsible for his crimes, then hers must be the final act of expiation.

I showed her the shower and tub, and she said, smiling, `` If you really don't mind, I think I'll get clean in the shower, then soak for a few minutes in your tub.

If internal responsibility suggests acceptance of the socialist ideal of equality, then external responsibility implies adherence to principles of ideological supranationalism.

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

If he is the child of nothingness, if he is the predestined victim of an age of atomic wars, then he will consult only his own organic needs and go beyond good and evil.

If it is an honest feeling, then why should she not yield to it??

If love reflects the nature of man, as Ortega Y Gasset believes, if the person in love betrays decisively what he is by his behavior in love, then the writers of the beat generation are creating a new literary genre.

If a child watched its progress he whispered, `` Hay, hay, load of hay -- make a wish and turn away '', and then stared rigidly in the opposite direction until the sound of the horses' feet returned no more.

If in any one calculation Ptolemy had had to invoke 83 epicycles all at once, while Copernicus never required more than one third this number, then ( in the sense obvious to Margenau ) Ptolemaic astronomy would be simpler than Copernican.

If to be innocent is to be helpless, then I had been -- as are we all -- helpless at the start.

Defoe then commented, `` If they Could Draw that young Gentleman into Their Measures They would show themselves quickly, for they are not asham'd to Say They want only a head to Make a beginning ''.

If the historian was convinced of his own correctness, then he should not allow his vision to become fogged by disturbing facts.

If man is actually the product of his environment and if science can discover the laws of human nature and the ways in which environment determines what people do, then someone -- a someone probably standing outside traditional systems of values -- can turn around and develop completely efficient means for controlling people.

If it will simply delay the debates until the qualifications are closed next spring, and then carry all the candidates on a tour of debates, it can provide a service to the state.

If they are to be commended for foresight in their planning, what then is the judgment of a town council that compounds this problem during the planning stage??

If the President of the United States really feels he won himself a `` lousy job '', then heaven help us all.

If we make it established custom that whenever butchery on the highways grows excessive, say beyond 25,000 per annum, then somebody is going to hang, it follows that the more eminent the victim, the more impressive the lesson.

If the raw population figures are crucially relevant, then it is idle to think of liberation, as idle as to suppose that Poland might liberate Russia.

If the UN troops are not mercenaries then the Hessians were not mercenaries either.

`` If they are here, then surely I have the right to be here '', Rousseau said.

If he failed to reach the riverbank in five minutes, say, then the skiffs would pull away and leave him groping in the mud.

If we had, then one of us would have had to go instead.

If our national interest lies in being able to fight and win a war rather than committing national suicide, then we must take a much more penetrating look at ballistic missiles.

If, for some reason such as economy, we are not going to develop aircraft nuclear propulsion with a sense of national urgency, then we should turn our effort to developing jet engines with a thrust-to-weight ratio of 12 or 15 to one.

If your pool is located on or near sloping ground, it may have natural drainage which is certainly more desirable than to be faced with the annual expense and labor of first pumping out the water and then scooping out all the debris.