In literature:
The foregoing examples are sufficient, although they could be multiplied indefinitely.
"The Science of Human Nature" by William Henry Pyle
The numbers of the sick multiplied beyond all example; even in the pest-affected cities of the Levant.
"Arthur Mervyn" by Charles Brockden Brown
Do this; multiply the loaves whose weight you see weighing down my balances.
"The Well of Saint Clare" by Anatole France
They multiplied with a rapidity hardly exceeded afterward by the Franciscans.
"Life of St. Francis of Assisi" by Paul Sabatier
And although the Lord sometimes multiply them in a secret manner, yet still the multitude stands to be true.
"The Covenants And The Covenanters" by Various
Prominent among these causes were its multiplied affiliations with the church.
"History of Rationalism Embracing a Survey of the Present State of Protestant Theology" by John F. Hurst
And the wonders multiplied.
"Born Again" by Alfred Lawson
They are like men multiplied.
"Modern American Prose Selections" by Various
Just find the cubic contents of Tecolote mountain and multiply it by three per cent.
"Rimrock Jones" by Dane Coolidge
Tales of this kind could be multiplied to almost any extent, but more need not be given.
"Welsh Folk-Lore a Collection of the Folk-Tales and Legends of North Wales" by Elias Owen
Evidences of prosperity and growing wealth began to multiply.
"A History of American Christianity" by Leonard Woolsey Bacon
Sponges multiply by the union of sexual product.
"The Handy Cyclopedia of Things Worth Knowing" by Joseph Triemens
The public institutions which multiplied at this period, tended to mitigate the spirit of party.
"The History of Tasmania, Volume I (of 2)" by John West
The measure then of mechanical effect is the mass of the body multiplied by the square of its velocity.
"Fragments of science, V. 1-2" by John Tyndall
Dividing hives to multiply colonies will not answer, 181.
"Langstroth on the Hive and the Honey-Bee" by L. L. Langstroth
War must be waged against rats and mice, or they will multiply and loot everything.
"How Girls Can Help Their Country" by Juliette Low
Sometimes it might multiply by two, while again it might multiply by a hundred.
"Where Half The World Is Waking Up" by Clarence Poe
The nervous connexions established among the viscera must further multiply their mutual influences; and so continually.
"Essays: Scientific, Political, & Speculative, Vol. I" by Herbert Spencer
On the contrary, the fit should be urged to multiply as much as possible.
"The Sexual Question" by August Forel
At the same time he wished not to multiply the vices of the system.
"The Journal of the Debates in the Convention which framed the Constitution of the United States, Volume II (of 2)" by James Madison
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In poetry:
They multiply above,
Making the mansions that our Lord prepared
And promised His redeemed, more beautiful
To us, the wayside pilgrims.
"Mrs. Frederick Tyler," by Lydia Howard Huntley Sigourney
They multiply above, with whom we walk'd
In tender friendship, and whose steadfast step,
Onward and upward, was a guide to us
In duty's path.
"Mrs. Frederick Tyler," by Lydia Howard Huntley Sigourney
Two travelers, each one with a light,
move in the darkness, silent, dumb.
The distance multiplies all night.
They count on meeting in the sum.
"For Schoolchildren" by Joseph Brodsky
His soul shall live secure on earth,
With secret blessings on his head,
When drought, and pestilence, and dearth
Around him multiply their dead.
"Psalm 41" by Isaac Watts
"And as the dew which leaves the morning flowers
Augments the after-rain--
And as the blooms which fall from summer bowers
Are multiplied again--
"Solemn Voices" by Thomas Buchanan Read
Thou hast permitted my invet'rate foes,
Without a cause, to multiply my woes,
And bring my days entirely to an end,
If thou dost not in time assistance lend.
"A Prayer, Against The Oppression Of One's Foe. " by Rees Prichard
In news:
Physician practices have " multiplier effect" on local economies.
The Department of Homeland Security (DHS) is hoping to enlist a new force multiplier in the fight against terrorism as the weather warms: the nation's 80 million recreational boaters.
Force Multiplier for the 21st Century.
New multiplier not a laughing matter to private schools.
Just when we thought we had it figured out, the MSHSAA threw another curve ball by passing the 1.35 multiplier .
It seems that they multiply even faster than rabbits do.
Phil Collier, the owner of A La Tomate, is a man multiply obsessed.
Getting It Right Involves More Than Simply Multiplying Vessel Size and Equipment.
Get more clients, make more money and multiply your business.
After several days of multiplying acreage, the Shingle Fire in Kane County has remained an 8,200-acre blaze for 2 days.
The problems have multiplied and work has slowed in the attempt to fix the seeping sewer line in the Siesta Addition.
If, however, you're one of those lucky city dwellers unafflicted by gephyrophobia — that is, the fear of crossing bridges — you'll find that your options multiply on the sunnier sides of the bay.
Things to do in the winter to multiply your edible gardening plants.
The rally was one of a quickly multiplying number of initiatives on the part of people responding to a sense that the time has come to be heard on issues ranging from the economy to hydrofracking.
China's debt problems multiply .
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In science:
Applying the chain rule shows that the multiplier of φ at P is equal to the multiplier of φh at h−1 (P ) (as long as both are ﬁnite points).
Explicit Descriptions of Quadratic Maps on $\pp^1$ defined over a field $K$
So for a quadratic rational map, either no multiplier is 1 (if the three ﬁxed points are distinct), or two multipliers are 1 (corresponding to a ﬁxed point of multiplicity two), or all three multipliers are 1 (corresponding to a ﬁxed point of multiplicity three).
Explicit Descriptions of Quadratic Maps on $\pp^1$ defined over a field $K$
We conclude that for quadratic rational maps, all three multipliers can be equal only if they are all equal to 1, or if they are all equal to −2; and if two multipliers are equal, they cannot be −1.
Explicit Descriptions of Quadratic Maps on $\pp^1$ defined over a field $K$
C2 ) if and only if two multipliers are equal but are not 1 or all three multipliers are 1 (case (b) of Theorem 1); and • the automorphism group is isomorphic to the symmetric group S3 if and only if all three multipliers are −2 (case (c) of Theorem 1).
Explicit Descriptions of Quadratic Maps on $\pp^1$ defined over a field $K$
We will frequently use the fact that a quadratic rational map is completely determined up to K -conjugacy by the three multipliers λ1 , λ2 , λ3 , or equivalently by the ﬁrst two symmetric functions on these multipliers σ1 and σ2 .
Explicit Descriptions of Quadratic Maps on $\pp^1$ defined over a field $K$
Then either all three multipliers are distinct, or exactly two multipliers are 1.
Explicit Descriptions of Quadratic Maps on $\pp^1$ defined over a field $K$
Recall that Aut(ψ) is trivial if and only if the three ﬁxed point multipliers are distinct or exactly two of the multipliers are 1.
Explicit Descriptions of Quadratic Maps on $\pp^1$ defined over a field $K$
First, assume that exactly two of the multipliers for ﬁxed points of ψ are 1, and let the third multiplier be λ 6= 1.
Explicit Descriptions of Quadratic Maps on $\pp^1$ defined over a field $K$
This map has a double ﬁxed point at z = 1 with multiplier 1, and a ﬁxed point at z = λ with multiplier λ.
Explicit Descriptions of Quadratic Maps on $\pp^1$ defined over a field $K$
So as long as the denominator Q(z ) does not vanish at any of the three multipliers, φ(z ) ∈ K (z ) has the correct ﬁxed point multipliers.
Explicit Descriptions of Quadratic Maps on $\pp^1$ defined over a field $K$
The multiplier at ∞ is zero, and since the other ﬁxed points satisfy z 2 + c = z , the other two multipliers sum to 2 and multiply to 4c.
Explicit Descriptions of Quadratic Maps on $\pp^1$ defined over a field $K$
The ﬁxed point multipliers for a map of the form φk,b (z ) are {2k − 1, 2k − 1, 1/k}, thus φk,b and φk′ ,b′ are conjugate over K if and only if k = k ′ Recall that a quadratic rational map φ(z ) has automorphism group C2 if and only if exactly two multipliers are equal and are not 1, or if all three multipliers are 1.
Explicit Descriptions of Quadratic Maps on $\pp^1$ defined over a field $K$
It is worth noting that any system of equations can be derived from a variational principle: Simply multiply each equation by an undetermined multiplier, add them together, and integrate over spacetime (for PDE’s) or time (for ordinary differential equations).
Action Principle for the Generalized Harmonic Formulation of General Relativity
Study of new concepts to read-out the ionization signal, such as large-area thick gas electron multipliers (GEMs), large-area gaseous photomultipliers (GPM) and CMOS pixel detectors coupled to electron multipliers. 4.
DARWIN: dark matter WIMP search with noble liquids
Indeed, a mod (216 ) == a&&216 , The choice of the multiplier a is not arbitrary: the multiplier is chosen so that ab − 1 is safeprime.
Using graphics processing units to generate random numbers
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