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original and form
It stood in its original form until 1882.
The Pantheon's interior, still in its original form, is truly majestic and an architectural triumph.
Most of Aristotle's work is probably not in its original form, since it was most likely edited by students and later lecturers.
The term " droid ", coined by George Lucas for the original Star Wars film and now used widely within science fiction, originated as an abridgment of " android ", but has been used by Lucas and others to mean any robot, including distinctly non-human form machines like R2-D2.
The United States Copyright Office defines copyright as " a form of protection provided by the laws of the United States ( title 17, U. S. Code ) to authors of " original works of authorship ".
Some scholars have hypothesized an original Proto-Indo-European pantheon, with the chief male god ( Di -) represented by the sky and thunder, and the chief female god ( feminine form of Di -) represented as the earth or fertile soil.
Some religious groups, such as the Association of Christian Schools International, opposed the ADA in its original form.
The solution, stationer, is an anagram of into tears, the letters of which have burst out of their original arrangement to form the name of a type of businessman.
Three separate sources were combined to form fr. 350, as mentioned above, including a prose paraphrase from Strabo that first needed to be restored to its original meter, a synthesis achieved by the united efforts of Otto Hoffmann, Karl Otfried Muller and Franz Heinrich Ludolf Ahrens.
Today, the Byzantine text-type is the subject of renewed interest as the original form of the text from which the Western and Alexandrian text-types were derived.
Because the original designer had left the company another employee completely redesigned most of the system, ( adding a display snow remover circuit, true 80 / 64 column text mode support, ( with different size letters for TRS-80 and CP / M mode, so that in TRS-80 mode the full screen was also used, not just a 64x16 portion of the 80x25 screen ) with an improved font set ( adding " gray scale " version of the TRS-80 mozaik graphics and many special PETSCII like characters ), and a more flexible and reliable floppy disk controller and keyboard interface plus many other small improvements ), also an enclosure was developed for the main computer system, ( in the form of a 19-inch rack for the Eurocards ) and for two floppy disk drives and the power supply.
The 1552 and later editions of the Book of Common Prayer omitted the form of anointing given in the original ( 1549 ) version in its Order for the Visitation of the Sick, but most twentieth-century Anglican prayer books do have anointing of the sick.
The American Federation of Musicians defines arranging as " the art of preparing and adapting an already written composition for presentation in other than its original form.
Because of the early origin of its original form, it does not address some Christological issues defined in the later Nicene and other Christian Creeds.
Austrian Germanist Rudolf Simek says that Bifröst either means " the swaying road to heaven " ( also citing bifa ) or, if Bilröst is the original form of the two ( which Simek says is likely ), " the fleetingly glimpsed rainbow " ( possibly connected to bil, perhaps meaning " moment, weak point ").
Beech became President of the Curtiss-Wright's airplane division and VP of sales, but became dissatisfied with being so far removed from aircraft production and quit to form Beechcraft, using the original Travel Air facilities and employing many of the same people.
Some classical rabbinical literature argues that this was the original form of the name and was a reference to the advanced age of Jacob when Benjamin was born.
Such a connection is possible if the original form of Boii belonged to a tribe of Proto-Indo-European speakers long before the time of the historic Boii.
The earliest parts of the book are possibly chapters 2 – 11, the story of the conquest ; more certain is that this section was then incorporated into an early form of Joshua that was part of then original Deuteronomistic history, written late in the reign of king Josiah ( reigned 640 – 609 BCE ); it seems clear that the book was not completed until after the fall of Jerusalem to the Babylonians in 586, and possibly not until after the return from the Babylonian exile late in the 6th century.
The book has a long and complex history, but its final form is probably due to a Priestly redaction ( i. e., editing ) of a Yahwistic original text some time in the early Persian period ( 5th century BCE ).
Later it moved into a more pastoral form, like Isaac Bickerstaffe's Love in a Village ( 1763 ) and Shield ’ s Rosina ( 1781 ), using more original music that imitated, rather than reproduced, existing ballads.
After Björkö came to be identified with ancient Birka, it has been assumed that the original name of Birka was simply Bierkø ( sometimes spelt Bjärkö ), an earlier form of Björkö.
Baudot's original code was adapted to be sent from a manual keyboard, and no teleprinter equipment was ever constructed that used it in its original form.
When using a cipher the original information is known as plaintext, and the encrypted form as ciphertext.

original and theorem
The original Nernst heat theorem makes the weaker and less controversial claim that the entropy change for any isothermal process approaches zero as T → 0:
Developed original resolution and unification based first order theorem proving, co-editor of the " Handbook of Automated Reasoning ", recipient of the Herbrand Award 1996
Using the above theorem it is easy to see that the original Borsuk Ulam statement is correct since if we take a map f: S < sup > n </ sup > → ℝ < sup > n </ sup > that does not equalize on any antipodes then we can construct a map g: S < sup > n </ sup > → S < sup > n-1 </ sup > by the formula
In Euclid's original approach, the Pythagorean theorem follows from Euclid's axioms.
Although flawed, Kempe's original purported proof of the four color theorem provided some of the basic tools later used to prove it.
Von Neumann's original proof used Brouwer's fixed-point theorem on continuous mappings into compact convex sets, which became a standard method in game theory and mathematical economics.
Baudhayana ( c. 8th century BCE ) composed the Baudhayana Sulba Sutra, the best-known Sulba Sutra, which contains examples of simple Pythagorean triples, such as:,,,, and as well as a statement of the Pythagorean theorem for the sides of a square: " The rope which is stretched across the diagonal of a square produces an area double the size of the original square.
Gödel's original proof of the theorem proceeded by reducing the problem to a special case for formulas in a certain syntactic form, and then handling this form with an ad hoc argument.
In modern logic texts, Gödel's completeness theorem is usually proved with Henkin's proof, rather than with Gödel's original proof.
The separation theorem is derived from the original form of the theorem.
Historical remark: In its original form by F. Riesz ( 1909 ) the theorem states that every continuous linear functional A over the space C ( 1 ) of continuous functions in the interval can be represented in the form
Since there is a one-to-one correspondence between Borel regular measures in the interval and functions of bounded variation ( that assigns to each function of bounded variation the corresponding Lebesgue-Stieltjes measure, and the integral with respect to the Lebesgue-Stieltjes measure agrees with the Riemann-Stieltjes integral for continuous functions ), the above stated theorem generalizes the original statement of F. Riesz.
A different generalization of Weierstrass ' original theorem is Mergelyan's theorem, which generalizes it to functions defined on certain subsets of the complex plane.
The virial theorem can be obtained directly from Lagrange's Identity as applied in classical gravitational dynamics, the original form of which was included in Lagrange's " Essay on the Problem of Three Bodies " published in 1772.
In essence, the theorem shows that a bandlimited analog signal can be perfectly reconstructed from an infinite sequence of samples if the sampling rate exceeds 2B samples per second, where B is the highest frequency of the original signal.
The theorem also leads to a formula for reconstruction of the original signal.
and the samples of x ( t ) are denoted by x ( nT ) for integer values of n. The sampling theorem leads to a procedure for reconstructing the original x ( t ) from the samples and states sufficient conditions for such a reconstruction to be exact.
The theorem describes two processes in signal processing: a sampling process, in which a continuous time signal is converted to a discrete time signal, and a reconstruction process, in which the original continuous signal is recovered from the discrete time signal.
According to the theorem, the reconstructed signal will match the original signal provided that the original signal contains no frequencies at or above this limit.
* If the highest frequency B in the original signal is known, the theorem gives the lower bound on the sampling frequency for which perfect reconstruction can be assured.
A distribution being " smoothed out " by summation, showing original Probability density function | density of distribution and three subsequent summations ; see Illustration of the central limit theorem for further details.

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