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integral and part
Next I refer to our program in space exploration, which is often mistakenly supposed to be an integral part of defense research and development.
In many societies, what we regard as corruption, favoritism, and personal influence are so accepted as consistent with the mores of officialdom and so integral a part of routine administrative practice that any attempt to force their elimination will be regarded by the local leadership as not only unwarranted but unfriendly.
the Athletic program at Carleton is considered an integral part of the activities of the College and operates under the same budgetary procedure and controls as the academic work.
Indeed, a study of the individual child is an integral part of the work of the elementary-school teacher, rather than merely an additional chore.
What Parker and his contemporaries -- Gillespie, Davis, Monk, Roach ( Tristano is an anomaly ), etc. -- did was to absorb the musical ornamentation of the older jazz into the basic structure, of which it then became an integral part, and with which it then developed.
As in the theory of perception, established in psycho-physiology, the eye is recognized as an integral part of the brain.
In Continental philosophy ( particularly phenomenology and existentialism ), there is much greater tolerance of ambiguity, as it is generally seen as an integral part of the human condition.
Confederates fought to protect southern society, and slavery as an integral part of it.
He is the so-called " Mad Arab " credited with authoring the imaginary book Kitab al-Azif ( the Necronomicon ), and as such is an integral part of Cthulhu Mythos lore.
* The Aluk religion in the Toraja society and the people of Tana Toraja, embrace religious rituals such as the funeral ceremony where a sacred cockfight, known as bulangan londong or saung, is an integral part of the ceremony and considered sacred because of the spilling of blood on the earth in spiritual appeasement.
Of particular interest to 20th-century music theorists is the attention he paid to silence as an integral part of music.
In fact, several of Alfred's laws contradict the laws of Ine that form an integral part of the code.
As this tension is an integral part of AA, Rudy and Greil argue that AA is best described as a quasi-religious organization.
The theory of special relativity predicts that any such device would allow communication from the future to the past, which raises problems of causality, unless the device used general relativistic curved spacetimes as an integral part.
These dots are an integral part of a letter, since they distinguish between letters that represent different sounds.
Before the break with papal authority in the 16th century, the Church of England was an integral part of the Western European church.
Ancient Balkh or Bactria was an integral part of Bactria – Margiana Archaeological Complex, and was occupied by Indo-Iranians.
Lipids are an integral part of our daily diet.
Also called the Megillah, the book is the basis and an integral part of the Jewish celebration of Purim.
The natural history collections were an integral part of the British Museum until their removal to the new British Museum of Natural History, now the Natural History Museum, in 1887.
Nevertheless, basic photography and video production are an integral part of the BJU cinema major.
This same belief is also an integral part of Methodist doctrine, and is connected with the doctrine of Justification.
They were dropped because besides being overseas departments, they were now overseas regions, and an integral part of France.
Kármán later helped create the Jet Propulsion Laboratory, and played an integral part in establishing Caltech as one of the world's centers for rocket science.
The concepts of hybridization are so versatile, and the variability in bonding in most organic compounds is so modest, that valence bond theory remains an integral part of the vocabulary of organic chemistry.

integral and any
Bézout's lemma is true in any principal ideal domain, but there are integral domains in which it is not true.
If is any unit vector, the projection of the curl of F onto is defined to be the limiting value of a closed line integral in a plane orthogonal to as the path used in the integral becomes infinitesimally close to the point, divided by the area enclosed.
If φ is C < sup > k </ sup >, then the inhomogeneous equation is explicitly solvable in any bounded domain D, provided φ is continuous on the closure of D. Indeed, by the Cauchy integral formula,
The same construction can be generalized to the field of fractions of any integral domain.
The Euler – Maclaurin formula provides expressions for the difference between the sum and the integral in terms of the higher derivatives ƒ < sup >( k )</ sup > at the end points of the interval m and n. Explicitly, for any natural number p, we have
Modern mathematics defines an " elliptic integral " as any function which can be expressed in the form
Software packages that perform rational arithmetic represent numbers as fractions with integral numerator and denominator, and can therefore represent any rational number exactly.
and where is the integral over any interval of length P.
If R is an integral domain then any two gcd's of a and b must be associate elements, since by definition either one must divide the other ; indeed if a gcd exists, any one of its associates is a gcd as well.
The Non-Aligned Yugoslavia was concerned about an eventual aggression from any of the superpowers, especially by the Warsaw Pact after the Prague Spring, so the Territorial Defense Forces were formed as an integral part of the total war military doctrine called Total National Defense.
An integral domain is a Bézout domain if and only if any two elements in it have a gcd that is a linear combination of the two.
A multiplicative identity is not required for the role of the integral domain ; this construction can be applied to any non-trivial commutative pseudo-ring with no zero divisors.
A sphere of any radius centered at zero is an integral surface of the following differential form:
Associated to any Hamiltonian is a Hamiltonian vector field ; the integral curves of the Hamiltonian vector field are solutions to Hamilton's equations.
The substance of any matter that has become an integral part of any human being has ceased to be the substance or reality of food and has become incorporated as an integral part of the physical manifestation or expression of that human person.
From a purely mathematical viewpoint, the Dirac delta is not strictly a function, because any extended-real function that is equal to zero everywhere but a single point must have total integral zero.
Powell claimed that the only way to stop the PIRA was for Northern Ireland to be an integral part of the United Kingdom, treated the same as any other of its constituent parts.
The recorder warning tone is required by law to be generated as an integral part of any recording device used for the purpose and is required to be not under the control of the calling party.

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