# integration

## Definitions

• WordNet 3.6
• n integration an operation used in the calculus whereby the integral of a function is determined
• n integration the action of incorporating a racial or religious group into a community
• n integration the act of combining into an integral whole "a consolidation of two corporations","after their consolidation the two bills were passed unanimously","the defendants asked for a consolidation of the actions against them"
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Webster's Revised Unabridged Dictionary
• Interesting fact: Intel is a shortened name for Integrated Electronics. The company's founders wanted to use the full name when they went into business in 1968, but it was already in use.
• Integration In the theory of evolution: The process by which the manifold is compacted into the relatively simple and permanent. It is supposed to alternate with differentiation as an agent in development.
• Integration The act or process of making whole or entire.
• Integration (Math) The operation of finding the primitive function which has a given function for its differential coefficient. See Integral.
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Century Dictionary and Cyclopedia
• Interesting fact: The name 'Intel' stems from the company's former name, 'Integrated Electronics'.
• n integration The act of integrating, or bringing together the parts of an integral whole; the act of segregating and bringing together similar particles.
• n integration In mathematics, the operation inverse to differentiation; the operation of finding the integral of a function or of an equation.
• n integration The inference of subcontrariety from “Some A is B” to “Some A is not B.”
• n integration The determination of the average rate of flow of a stream. On account of the varying friction against the bottom, sides, and overlying air, this value, as a rule, differs from the rate at any particular place in the cross-section of the stream.
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## Quotations

• Frank Perdue
“If you believe in unlimited quality and act in all your business dealings with total integrity, the rest will take care of itself.”
• Ayn Rand
“A building has integrity just like a man. And just as seldom.”
• Peter Scotese
“Integrity is not a 90 percent thing, not a 95 percent thing; either you have it or you don't.”
• Henry David Thoreau
“The laboring man has not leisure for a true integrity day by day.”
• Source Unknown
“A person is not given integrity. It results from the relentless pursuit of honesty at all times.”
• Source Unknown
“The slow man with integrity will ultimately catch the swift one who has none.”

## Etymology

Webster's Revised Unabridged Dictionary
L. integratio, a renewing, restoring: cf. F. intégration,

## Usage

### In literature:

Decaen rose rapidly, by reason not merely of his bull-dog courage and stubborn tenacity, but also of his intelligence and integrity.
"The Life of Captain Matthew Flinders" by Ernest Scott
Events went on in the little household as if Sally had become an integral part of it already.
"The Fallen Leaves" by Wilkie Collins
The cause of integrity should never be despaired of.
"Imogen" by William Godwin
Individual initiative and hard work, honesty and integrity, must be recognized and rewarded.
"Dorothy's Mystical Adventures in Oz" by Robert J. Evans
Let INTEGRITY and UPRIGHTNESS preserve me, for I wait on thee.
"Female Scripture Biographies, Vol. I" by Francis Augustus Cox
We feel that this man and falsehood are impossible companions, and our faith in his integrity is perfect and absolute.
"The Atlantic Monthly, Volume 1, Issue 2, December, 1857" by Various
What then can we suppose was the reason, that neither indignation, nor integrity, nor resentment, ever before directed a motion like this?
"The Works of Samuel Johnson, Vol. 11." by Samuel Johnson
Integrity and independency, however mistaken, are entitled to praise.
"Four Early Pamphlets" by William Godwin
From this time Franklin rapidly gained in public esteem for his integrity, his sagacity, and his unrivalled good sense.
"Beacon Lights of History, Volume XI" by John Lord
Under it the signatories in 1887 guarantee the integrity of their respective territories.
"The Nuttall Encyclopaedia" by Edited by Rev. James Wood
I am convinced that the integrity of the Union can only be preserved by withholding the armed hand at this crisis.
"Fort Lafayette or, Love and Secession" by Benjamin Wood
He was not a man of strict integrity.
"The American Indian as Participant in the Civil War" by Annie Heloise Abel
The Americans alone held aloof, proclaiming the policy of Chinese integrity and the Open Door.
"The Problem of China" by Bertrand Russell
But integrity, and a liberal vein of genius, are mine: and the man of fortune makes his court to me, who am but poor.
"The Works of Horace" by Horace
But all that is great, or good, or valuable, in this world, must be attained by labour, perseverance, courage, and integrity.
"The American Quarterly Review" by Various
It is not individual; it is not integral; it is social, and marks half of you and half of others.
"Browning and the Dramatic Monologue" by S. S. Curry
"The Life and Letters of Mary Wollstonecraft Shelley, Volume II (of 2)" by Florence A. Thomas Marshall
However seductive the temptations which may beset you, never compromise your integrity.
"Nature and Culture" by Harvey Rice
It is my firm conviction that the only way to remedy it is to make the elements of physical science an integral part of primary education.
"Aphorisms and Reflections from the Works of T. H. Huxley" by T. H. Huxley
In spite of these afflictions Job retains his integrity and ascribes no wrong to God.
"Encyclopaedia Britannica, 11th Edition, Volume 15, Slice 4" by Various
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### In poetry:

To be unloved gives sweet relief;
The one integrity
Of soul is to be lone,
Inviolate, and free.
"Lovers" by Mary Eliza Fullerton
All do him honor, who regard
Integrity sincere,
But they who knew his virtues best,
While fond remembrance rules the breast,
Will hold his image dear.
"Hon. Phillip Ripley," by Lydia Howard Huntley Sigourney
A youngster at school, more sedate than the rest,
Had once his integrity put to the test;
And asked him to go and assist in the job.
"Pity For Poor Africans" by William Cowper
Too soon he fell! Was he not born to prove
What manhood and integrity might be--
How one from all base elements apart
Might walk serene, in purity of heart,
His face the bright transparency of love
And sympathy?
"The Student Gone" by Hattie Howard
Now the bar was pretty quiet, and everybody heard
The peculiar integration of this adjectival word,
But no-one there was laughing, and me - I wasn't game,
So I just sits back and lets them think I spoke the bloody same.
"Tumba Bloody Rumba" by John O Brien
Because many a hungry soul he relieved while in distress,
And for doing so I hope the Lord will him bless,
For his kindness towards the poor people in Dundee,
Besides for his love towards the temperance cause, and his integrity.
"The Funeral of the Late Ex-Provost Rough, Dundee" by William Topaz McGonagall

### In news:

Integrated cashiering and payment processing will enhance revenue collection and customer service throughout the city's seven payment centers.
Real Time Services, a New York-based audiovisual systems integrator, welcomes Joy Caspar as its senior sales engineer.
In her new position, Caspar will be responsible for the engineering, development, and planning of integrated AV systems for clients in the education, medicine, law, and finance.
Using a military commission to try Sept 11 terrorists fails to demonstrate the integrity of the nation's justice system.
Of course the Catholic Church's attachment to Jesus as a celibate is most integral to church teachings.
The partnership hopes to deliver create integrated engineering design packages for low-cost production of ethanol from non-food-based feedstocks.
The CEN -UPS1250 from Crestron is an uninterruptible power supply and conditioner designed to protect and monitor a fully integrated system.
New management platform helps Louisville utility with environmental data integration.
Integrated Microwave Technologies announced that it has achieved ISO 9001:2008 Quality Management certification for its Mt Olive production facility.
A more integrated Europe is heading for a showdown with Britain.
The strategy and design for the Facebook integration on CharlotteRusse .com was created by the Fluid agency team.
Dave McMillen, Sales Manager for Advanced Analytical and Analyzer Systems Integration at Yokogawa, explains the companies newest offering -- the GC8000 -- to senior digital editor Traci Purdum.
Kewill has integrated its existing shipper services with Stamps.com to provide customers with easier access to domestic and international parcel services.
An integrated system combining advanced analytics and data storage in a cloud infrastructure is now available for geospatial intelligence analysts, who often are under pressure to derive value from vast amounts of data.
LG CNS , the integration arm of LG, has named Tony Turiello to the position of senior account executive of business development.
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### In science:

To obtain degenerations of complete varieties we need to start from a bounded tropical manifold (B , P ), where B denotes the underlying singular integral aﬃne manifold and P is the decomposition into integral polyhedra, together with an (in general multi-valued) integral piecewise aﬃne function ϕ.
An invitation to toric degenerations
To describe in a few words how motivic integration is different from classical integration it seems best to begin by pointing out that the ring that provides values for integrals is not the real ﬁeld but a Grothendieck ring.
Integration in algebraically closed valued fields
As in the classical theory of integration, this strategy requires some form of Fubini’s theorem: for a well-behaved integration, an integral should give the same value when it is evaluated along different orders of variables.
Integration in algebraically closed valued fields
The integration over the emission times te (represented in the different snapshot ﬁles) requires an ex tra beaming factor and a factor of c to transform the total integral to a volume integral.
From blast wave to observation
To integrate F over Ui we ﬁrst multiply it by the volume form φV which acts as the integration measure for the integral.
A Simple Introduction to Particle Physics Part II
The volume form on the manifold determines the orientation of the integral, and the integral is independent of the coordinate functions chosen - the Jacobian allows us to transform the integral from one coordinate system to another.
A Simple Introduction to Particle Physics Part II
Notice that the integral on the left is an n-form integrated over an n-dimensional space, whereas the right is an (n − 1)-form integrated over an (n − 1)-dimensional space, so the integral makes sense on both sides.
A Simple Introduction to Particle Physics Part II
Furthermore, as we said previously, we can map the standard simplexes into a manifold M to integrate over a neighborhood of M, and so by using everything we know about integration, we can generalize this to integrals of forms on arbitrary manifolds.
A Simple Introduction to Particle Physics Part II
When the system is nearly integrable, the Hamiltonian for the unperturbed part becomes much larger than that of the perturbed part, which enables the method to accomplish a very high accuracy in integrating the equations of motion, compared with conventional symplectic integrators.
FAST: A Fully Asynchronous Split Time-Integrator for Self-Gravitating Fluid
It is important that the integration over the lapse function N runs along the imaginary axis from −i∞ to +i∞ because this Euclidean path integral represents, in fact, the transformed version of the integral over metrics with Lorentzian signature.
Tunneling cosmological state revisited: Origin of inflation with a non-minimally coupled Standard Model Higgs inflaton
The Fourier representation of these delta functions in terms of the integral over the conjugated Lagrange multipliers – the lapse NL (and shift) functions – implies an integration with limits at inﬁnity, −∞ < NL < ∞, which explains the range of integration over the Euclidean N .
Tunneling cosmological state revisited: Origin of inflation with a non-minimally coupled Standard Model Higgs inflaton
In fact, the formal Euclidean path integral (6) is a transformed version of the microcanonical path integral over Lorentzian metrics, so that its lapse function integration runs along the imaginary axis from −i∞ to +i∞ 3 .
Tunneling cosmological state revisited: Origin of inflation with a non-minimally coupled Standard Model Higgs inflaton
Most important, this completes the GKMMM description of SW theory in terms of integrability theory with the help of exact BS integrals, and provides an extended manifestation of the basic principle which states that the effective actions are the tau-functions of integrable hierarchies.
Matrix Model Conjecture for Exact BS Periods and Nekrasov Functions
As mentioned, after we tilt or rotate the integration contour into the positive imaginary plane for the left integral, and negative imaginary plane for the right integral, all the oscillatory behavior in the UV becomes well-behaved exponential decay.
Primordial Non-Gaussianities from Inflation Models
Therefore we have to keep the whole integrals in the Eq. (65) and Eq. (71), i.e. in each integral we can not integrate the last term out because otherwise the integral does not converge.
Using pseudo-parabolic and fractional equations for option pricing in jump diffusion models
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