pivotal

Definitions

  • WordNet 3.6
    • adj pivotal being of crucial importance "a pivotal event","Its pivotal location has also exposed it to periodic invasions"- Henry Kissinger","the polar events of this study","a polar principal"
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Webster's Revised Unabridged Dictionary
    • a Pivotal Of or pertaining to a pivot or turning point; belonging to, or constituting, a pivot; of the nature of a pivot; as, the pivotalopportunity of a career; the pivotal position in a battle.
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Century Dictionary and Cyclopedia
    • pivotal Of the nature of or forming a pivot; belonging to or constituting a pivot, or that upon which something turns or depends: as, a pivotal question; a pivotal State in an election.
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Chambers's Twentieth Century Dictionary
    • adj Pivotal of the nature of a pivot: acting as a pivot
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Quotations

  • W. Arthur Porter
    W. Arthur Porter
    “The INNOVATION point is the pivotal moment when talented and motivated people seek the opportunity to act on their ideas and dreams.”
  • Susan B. Anthony
    Susan B. Anthony
    “Suffrage is the pivotal right.”
  • Caroline Bird
    Caroline Bird
    “Femininity appears to be one of those pivotal qualities that is so important no one can define it.”

Etymology

Chambers's Twentieth Century Dictionary
Fr. dim. of It. piva, a pipe, a peg, a pin—Low L. pipa.

Usage

In literature:

And a sort of search-light that swung on a pivot.
"The Real Adventure" by Henry Kitchell Webster
Of little need to tell of the privations which the pivotal state of the Confederacy went through.
"The Littlest Rebel" by Edward Peple
The pivots on which the paddle-wheel turns.
"New York Times Current History: The European War, Vol 2, No. 1, April, 1915" by Various
And that third brick, which looked so solidly placed, turned as upon a pivot and swung out sideways.
"A Woman Named Smith" by Marie Conway Oemler
As will be seen, the gongs are mounted on posts which are carried on levers pivoted to the ringer frame.
"Cyclopedia of Telephony & Telegraphy Vol. 1" by Kempster Miller
The doors of the reception hall had been flung back on noiseless pivots by unseen hands.
"A Friend of Caesar" by William Stearns Davis
She pivoted, arms tossing, face aflame.
"The Poor Little Rich Girl" by Eleanor Gates
As suggested in an earlier chapter, the teacher should have prepared a list of pivotal questions as a part of her lesson plan.
"How to Teach Religion" by George Herbert Betts
The whole is mounted on a metal cradle, which turns on pivots.
"Scientific American Supplement, No. 441, June 14, 1884." by Various
Every point of life is a pivot on which turns the whole action of our after-lives; and so, indeed, of the after-lives of the whole world.
"The Man Without a Country and Other Tales" by Edward E. Hale
The editor is the pivot of a magazine.
"A Dutch Boy Fifty Years After" by Edward Bok
Why must he always be the central pivot of a whirlpool of excitement?
"Kenny" by Leona Dalrymple
They were not hung upon hinges, like modern doors, but, like those of the classical nations, turned upon pivots.
"The Seven Great Monarchies Of The Ancient Eastern World, Vol 2. (of 7): Assyria" by George Rawlinson
Thus its name must be changed, as a prelude to using the new pivot.
"Music As A Language" by Ethel Home
Here the guiding theme is the pivot upon which the entire work turns.
"The Opera" by R.A. Streatfeild
This sudden turn of the political kaleidoscope was a pivotal point in the life of Ary Scheffer.
"Little Journeys to the Homes of the Great, Volume 4 (of 14)" by Elbert Hubbard
Her gaze pivoted slowly until it encompassed the arc of a half-circle, so that she faced Hollister squarely.
"The Hidden Places" by Bertrand W. Sinclair
The handle turns on a pivot and the end is drawn upwards by means of a bent twig, or sapling, which acts as a spring.
"The Wild Tribes of Davao District, Mindanao" by Fay-Cooper Cole
The hat slowly pivoted a head into view.
"Sunny Slopes" by Ethel Hueston
Sssuri pivoted slowly, studying the circle of buildings about them.
"Star Born" by Andre Norton
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In poetry:

As, dimly seen, the pirate of the brook--
The pike, whose jaunty hulk denotes his speed--
Swings pivoting about, with wary look
Of low and cunning greed.
"A Country Pathway" by James Whitcomb Riley
When I undertake to tell the best, I find I cannot,
My tongue is ineffectual on its pivots,
My breath will not be obedient to its organs,
I become a dumb man.
"Carol Of Words" by Walt Whitman
How many dawns, chill from his rippling rest
The seagull's wings shall dip and pivot him,
Shedding white rings of tumult, building high
Over the chained bay waters Liberty—
"To Brooklyn Bridge" by Harold Hart Crane
The Pyramids abide; but through the shaft
That held the polar pivot, eye to eye,
Look now — blank nothingness! As though Change laughed
At man's presumption and his puny craft,
The star has slipped its leash and roams the sky.
"The Old Pole Star" by Edith Wharton

In news:

Obama's Myanmar visit is pivotal for Asia policy.
China's local delegates revel in their moment close to power during pivotal party congress.
Abiomed Receives FDA IDE Approval for Use of New Impella RP in Pivotal Clinical Study.
Pancreatic Cancer Drug Tanks in Pivotal Study.
Pivotal Patent Case Heads to Court.
Nonwhite voters and cultural shifts make 2012 election pivotal .
Second quarter likely pivotal .
It might take a few series for everything to settle in, but there will be a pivotal quarter in today's Oklahoma-Baylor game.
NORMAN — It might take a few series for everything to settle in, but there will be a pivotal quarter in today's Oklahoma-Baylor game.
It would be easy to say Marvin Lewis faces a pivotal season because the Bengals coach is in the final year of a two-year extension.
On the ground in Tripoli, we saw an opportunity to advance US interests in a pivotal region.
With an Obama victory, Wall Street pivots to plan B. Obama Girls' Role: Not to Speak, but to Be Spoken Of.
Egypt and Morsy proved 'pivotal' in Gaza cease-fire talks.
Washington's inability to resolve its basing arrangements on Okinawa underscores the challenges for Obama's strategic "pivot" toward the Pacific.
Hot Wings randomly brought up the movie ' Scarface ' this morning, pivoting from a conversation about how cool it would be to have a job as a Foley artist.
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In science:

Nontrivial upper bounds on its expected number of pivot steps on general polytopes do not exist.
Two New Bounds on the Random-Edge Simplex Algorithm
None of the existing results exclude the possibility of both Random-Facet and Random-Edge being the desired (expected) polynomial-time pivot rules.
Two New Bounds on the Random-Edge Simplex Algorithm
Let π be the random variable defined as the directed path in D, starting at s and ending at the sink vopt of D, induced by the Random-Edge pivot rule.
Two New Bounds on the Random-Edge Simplex Algorithm
C (G ) is a strict pivotal category, in other words verifies the conditions of definitions 2.1 and 2.2 of [BW2].
Categorical Groups, Knots and Knotted Surfaces
Recall that the category C (G ) is a strict pivotal category.
Categorical Groups, Knots and Knotted Surfaces
In a pivotal fusion category C one defines for any ob ject M ∈ C its dimension dM ∈ k , see .
Pre-modular categories of rank 3
For an increasing event A, a triangle t is pivotal if, when empty, the event A does not occur but if fully occupied then it does.
Random Cluster Models on the Triangular Lattice
A| denotes the number of pivotal triangles for the event A.
Random Cluster Models on the Triangular Lattice
It is clear that the basic “chain of sausages” picture holds in this context (with paths of bonds replaced by clusters of triangles) and at the endpoint of each sausage, a pivotal triangle.
Random Cluster Models on the Triangular Lattice
Recall that the first move is played at the site that is most likely to be pivotal.
Random-Turn Hex and other selection games
The probability that a site is pivotal is not scale invariant (for larger boards, the probability that a site is pivotal is smaller).
Random-Turn Hex and other selection games
Thus, a vertex is pivotal if and only if the path from that vertex to the root has the property that every sibling of a vertex along that path is T or F as the level is odd or even.
Random-Turn Hex and other selection games
Note that the event “v is pivotal” is independent of labels on the subtree below v .
Random-Turn Hex and other selection games
Let rt (u) be the conditional probability that a vertex u is pivotal given the labels that have been set prior to move t.
Random-Turn Hex and other selection games
The following lemma is pivotal for the computations which follow.
Flows and ferromagnets
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