( Aside from its historic role as a total-computable-but-not-primitive-recursive function, Ackermann's original function is seen to extend the basic arithmetic operations beyond exponentiation, although not as seamlessly as do variants of Ackermann's function that are specifically designed for that purpose — such as Goodstein's hyperoperation sequence.

A paperback collection of the original sequence, The Life and Times of the Shmoo, became a bestseller for Simon & Schuster.

But " having distance 0 " is an equivalence relation on the set of all Cauchy sequences, and the set of equivalence classes is a metric space, the completion of M. The original space is embedded in this space via the identification of an element x of M with the equivalence class of sequences converging to x ( i. e., the equivalence class containing the sequence with constant value x ).

Ephrem did not comment on all passages in the Diatessaron, and nor does he always quote commentated passages in full ; but for those phrases that he does quote, the commentary provides for the first time a dependable witness to Tatian's original ; and also confirms its content and their sequence.

In other words, when you pass a sequence to a routine, initially only a reference to it is passed, but at the point the routine modifies this sequence parameter the sequence is copied and the routine updates only a copy of the original.

The finished version of the film was significantly different from the original screenplay drafts as Bruce Lee revised much of the script himself, including having written and directed the film's opening Shaolin Monastery fight sequence.

Heterochrony represents a gradual alteration in the original phylogenetic sequence due to embryonic adaptation.

Initially, the opening sequence included all five characters from the original film, but, in an effort to save time and money, all but Ash and Linda were cut from the final draft.

Robinson says that John's chronology is consistently more likely to represent the original sequence of events.

The original orchestral score was composed by Michael Kamen, but the soundtrack includes several songs by Queen, like " Princes of the Universe ", which was also used in the Highlander television series title sequence.

The illustration she used of the Cogul painting leaves out a number of figures, human and animal, and the original is more likely a sequence of superimposed but unrelated illustrations, rather than a depiction of a single scene.

Compression is successful if the resulting sequence is shorter than the original sequence plus the map needed to decompress it.

The original B-O-B ' sequence is changed by the integration to B-O-P '- phage DNA-P-O-B '.

Chemical damage to DNA occurs naturally as well, and cells use DNA repair mechanisms to repair mismatches and breaks in DNA — nevertheless, the repair sometimes fails to return the DNA to its original sequence.

Nevertheless, the repair sometimes fails to return the DNA to its original sequence.

The ISR will perform any processing required based on the source of the interrupt before returning to the original instruction sequence.

Vestiges of the original alphabetical layout remained in the " home row " sequence DFGHJKL.

In the 1970s and 1980s, Industrial Light & Magic often used stop motion model animation for films such as the original Star Wars trilogy: the chess sequence in Star Wars, the Tauntauns and AT-AT walkers in The Empire Strikes Back, and the AT-ST walkers in Return of the Jedi were all stop motion animation, some of it using the Go films.

Star Trek: The Animated Series was the only Star Trek series not to feature a cold open (" teaser ") and started directly with the title sequence ( although some overseas versions of the original live action series, such as that run by the BBC in the U. K. in the 1960s and 1970s, ran the teaser after the credits ).

Shots from the show's original opening credit sequence.

The original opening sequence was made in 1993 for the first season and remained unchanged throughout the series, until David Duchovny left the show as a main character in season seven.

He had not yet undertaken the great exploit of his later years, the rediscovery of the ancient Inca highway, the route of Pizarro in Peru, but he had climbed to the original El Dorado, the Andean lake of Guatemala, and he had scaled the southern Sierra Nevada with its Tibetan-like people and looked into the emerald mines of Muzo.

Although the wood has been changed to coal, much of it still retains its original cell structure.

But he painted some of the boldest and most original pictures of his time, and even after nearly half a century, the tense, tormented world he put on canvas has lost none of its fascination.

Petitioner was not entitled, either in the administrative hearing at the Department of Justice or at his trial, to inspect the original report of the Federal Bureau of Investigation, since he was furnished a resume of it, did not challenge its accuracy, and showed no particular need for the original report.

The original machine, bearing its famous serial number, is still on exhibition at the Brown & Sharpe Precision Center in Providence.

It stood in its original form until 1882.

The historical sign tells its story, but nothing gets interest across as well as some of the original historical items or places themselves which still have the character of the period covered.

The original electrocardiograph primarily indicates irregularities in the heartbeat, but today's techniques allow exact measurements of the flow of blood through the aorta, dimensioning of the heart and its chambers, and a much more detailed study of each heartbeat.

Spectra were also obtained from a third sample of Af which had been diluted to three times its original volume with powdered, anhydrous alundum ( Af ).

The Pantheon's interior, still in its original form, is truly majestic and an architectural triumph.

He suggested that without the Socialist Party ever gaining a national victory, most of its original program has come to pass under both major parties.

Each dot on magnification resumed its original condition as a drawing, a printed page, or a manuscript.

The Hopkinsian universal disinterested benevolence, although holding to original sin and the doctrine of election, inspired its adherents to heroic endeavours for others, looked for the early coming of the Millennium, and was paralleled by the confidence in man's ability cherished by the Unitarians, Emerson, and the Transcendentalists.

In 1851, he represented Alton & Sangamon Railroad in a dispute with one of its shareholders, James A. Barret, who had refused to pay the balance on his pledge to buy shares in the railroad on the grounds that the company had changed its original train route.

Lincoln successfully argued that the railroad company was not bound by its original charter in existence at the time of Barret's pledge ; the charter was amended in the public interest to provide a newer, superior, and less expensive route, and the corporation retained the right to demand Barret's payment.

Most of Aristotle's work is probably not in its original form, since it was most likely edited by students and later lecturers.

The category's original name was Best Art Direction and was changed to its current name for the 85th Academy Awards, with the Art Director's branch being renamed the Designer's branch.

Like many games of its time, Asteroids contains several bugs that were mostly the result of the original programmers underestimating the game's popularity or the skill of its players.

The term when adopted into ecclesiastical usage retained much of its original significance.

The Aegean was the site of the original democracies, and its seaways were the means of contact among several diverse civilizations of the Eastern Mediterranean.

While the group only recorded one album together as the Analog Brothers, a few bootlegs of its live concert performances, including freestyles with original lyrics, have occasionally surfaced online.

If the original word was capitalised, then the first letter of its abbreviation should retain the capital, for example Lev.