In On the Infinite, David Hilbert hypothesized that the Ackermann function was not primitive recursive, but it was Ackermann, Hilbert ’ s personal secretary and former student, who actually proved the hypothesis in his paper On Hilbert ’ s Construction of the Real Numbers.

On the Infinite was Hilbert ’ s most important paper on the foundations of mathematics, serving as the heart of Hilbert's program to secure the foundation of transfinite numbers by basing them on finite methods.

J. B. Curtis in his 1979 paper " On Job's Response to Yahweh ", argues that Job's final responses to Yahweh are a total rejection of Yahweh rather than an expression of repentance, and translates Job 42: 6 as " Therefore I feel loathing contempt and revulsion ( toward you, O God ); and I am sorry for frail man.

It began in the 1948 paper, " On the Problem of the Molecular Theory of Superconductivity " where Fritz London proposed that the phenomenological London equations may be consequences of the coherence of a quantum state.

Rebuffed by William Thiselton-Dyer, the Director at Kew, because of her gender and her amateur status, Beatrix wrote up her conclusions and submitted a paper On the Germination of the Spores of the Agaricineae to the Linnean Society in 1897.

On June 30, 1945, before ENIAC was made, mathematician John von Neumann distributed the paper entitled First Draft of a Report on the EDVAC.

Building on the work of Clausius, between the years 1873-76 the American mathematical physicist Willard Gibbs published a series of three papers, the most famous one being the paper On the Equilibrium of Heterogeneous Substances.

On paper, using classical notation, this is usually done all in one step.

On the other hand, Emil Post's 1936 paper had appeared and was certified independent of Turing's work.

Turing adds another definition, Rosser equates all three: Within just a short time, Turing's 1936 – 37 paper " On Computable Numbers, with an Application to the Entscheidungsproblem " appeared.

In his 1868 paper " On Governors ", J. C. Maxwell ( who discovered the Maxwell electromagnetic field equations ) was able to explain instabilities exhibited by the flyball governor using differential equations to describe the control system.

His first paper, " On a recent formation of freshwater limestone in Forfarshire ", was presented in 1822.

On one hand, there are transmitted versions and commentaries that date back two millennia ; on the other, there are ancient bamboo, silk, and paper manuscripts that archeologists discovered in the last century.

Such was the time taken in peer-reviewing the paper for Nature that this was preceded by a 1972 essay by Maynard Smith in a book of essays titled On Evolution.

On the local level, a butcher may commonly break down larger animal meat into smaller manageable cuts, and pre-wrap them for commercial sale or wrap them to order in butcher paper.

On September 22, 2011, a paper from the OPERA Collaboration indicated detection of 17 and 28 GeV muon neutrinos, sent 730 kilometers ( 454 miles ) from CERN near Geneva, Switzerland to the Gran Sasso National Laboratory in Italy, traveling faster than light by a factor of 2. 48 × 10 < sup >− 5 </ sup > ( approximately 1 in 40, 000 ), a statistic with 6. 0-sigma significance.

The first paper from his years of study in Paris appeared in Frankfurt am Main in 1816, under the title of Über das Conjugationssystem der Sanskritsprache in Vergleichung mit jenem der griechischen, lateinischen, persischen und germanischen Sprache ( On the Conjugation System of Sanskrit in comparison with that of Greek, Latin, Persian and Germanic ) ( Windischmann contributed a preface ).

Three years later came the paper that would make his name famous, Sur les équations du mouvement relatif des systèmes de corps ( On the equations of relative motion of a system of bodies ).

On paper, there were 100, 000 or so Volunteers enrolled after the conscription crisis of 1918.

On awakening he appeared to himself to have a distinct recollection of the whole, and taking his pen, ink, and paper, instantly and eagerly wrote down the lines that are here preserved.

After reading from Purchas's book, " The Author continued for about three hours in a profound sleep, at least of the external senses, during which time he had the most vivid confidence, that he could not have composed less than from two or three hundred lines ... On Awaking he appeared to himself to have a distinct recollection of the whole, and taking his pen, ink, and paper, instantly and eagerly wrote down the lines that are here preserved.

In 1917, Albert Einstein established the theoretical foundations for the laser and the maser in the paper Zur Quantentheorie der Strahlung ( On the Quantum Theory of Radiation ); via a re-derivation of Max Planck ’ s law of radiation, conceptually based upon probability coefficients ( Einstein coefficients ) for the absorption, spontaneous emission, and stimulated emission of electromagnetic radiation ; in 1928, Rudolf W. Ladenburg confirmed the existences of the phenomena of stimulated emission and negative absorption ; in 1939, Valentin A. Fabrikant predicted the use of stimulated emission to amplify “ short ” waves ; in 1947, Willis E. Lamb and R. C. Retherford found apparent stimulated emission in hydrogen spectra and effected the first demonstration of stimulated emission ; in 1950, Alfred Kastler ( Nobel Prize for Physics 1966 ) proposed the method of optical pumping, experimentally confirmed, two years later, by Brossel, Kastler, and Winter.

In his 1861 paper On Physical Lines of Force he modelled these magnetic lines of force using a sea of molecular vortices that he considered to be partly made of aether and partly made of ordinary matter.

Maxwell's equations are named after the Scottish physicist and mathematician James Clerk Maxwell, since in an early form they are all found in a four-part paper, " On Physical Lines of Force ", which he published between 1861 and 1862.

On Friday nights the Zimmermann family would take the subway into Manhattan to see the vaudeville show at the Palace Theatre, where Merman discovered Blossom Seeley, Fanny Brice, Sophie Tucker, and Nora Bayes.

On the Senate side, two separate subway systems exist.

On 23 November 1954 an edition of The Goon Show entitled ' The Last Tram ' featured a driver and conductress who hid in the subway for 2½ years in order to ensure they were London's last tram.

On January 14, 2006, when Garrett was arrested on a Los Angeles subway platform for not having a ticket, police found drugs in his possession.

On December 7, 1980, the day before the killing, Chapman accosted singer-songwriter James Taylor at the 72nd Street subway station.

* In On the Road, Riverdale-educated Jack Kerouac writes about getting off at a subway stop in Riverdale: " Filled with dreams of what I'd do in Chicago, in Denver, and then finally in San Fran, I took the Seventh Avenue Subway to the end of the line at 242nd Street, and there took a trolley into Yonkers ; in downtown Yonkers I transferred to an outgoing trolley and went to the city limits on the east bank of the Hudson River.

On his first day as mayor, Jan. 1, 1966, the Transport Workers Union of America ( TWU ) led by Mike Quill shut down the city with a complete halt of subway and bus service.

On December 28, 2005, Pettigrew was the victim of an attempted mugging while he was waiting for a train in the Montreal subway station.

On October 27, 1904, local and express service opened on the original subway in Manhattan, following the route of the present IRT Lexington Avenue Line from City Hall to Grand Central – 42nd Street.

* On the same plaza, the homonymous subway station can be found, which is used by some characters to escape.

On 4 May 1885, the MDR opened a pedestrian subway running from the station beneath the length of Exhibition Road, giving sheltered access to the newly built museums for a toll of 1 penny.

* 1995 On March 20, the Aum Shinrikyo cult spread Sarin nerve gas on the Tokyo subway system ; 12 people were killed and thousands affected ( see 1995 Tokyo Subway Attacks ).

On the Tokyo subway maps, Hibiya Station is marked as an interchange and is linked to Yūrakuchō by underground passages.

On this day, the subway closed the temporary terminal at Manseibashi Station and made Kanda Station the new terminus.

On July 10, 1905, the connection between the IRT Lenox Avenue Line and IRT White Plains Road Line ( which was previously served by the Third Avenue El ) opened, allowing subway service from Manhattan to the Bronx.

* On August 1, 1920, subway service on the Brooklyn – Manhattan Transit Corporation's Brighton Beach Line officially began upon opening of Montague Street Tunnel and a two track line connecting Prospect Park and DeKalb Avenue.

On May 30, 1919, Brighton Beach Line service was extended west to the area once known as West Brighton, now the heart of what is left of the entertainment area of Coney Island, where it occupied part of New West End Terminal, better known as the Stillwell Avenue Terminal, the structure which serves as a union terminal for the four subway lines that run to Coney Island.

On May 20, 2009, Delaware River Port Authority ( DRPA ) Chairman John Estey announced that the DRPA would renovate and modernize the PATCO subway station under Franklin Square.

On April 1, 1903, over a year before its first subway line opened, the IRT acquired the pre-existing elevated Manhattan Railway by lease, gaining a monopoly on rapid transit in Manhattan.

On 18 December 2000, Cityplace Station, the southwest's first commercial subway station was opened along the Red Line underneath Cityplace Tower just northeast of downtown.

Jennifer Lopez's debut album On the 6, a reference to the 6 subway line she used to take growing up in Castle Hill was released on June 1, 1999, and reached the top ten of the Billboard 200.

On October 15, 1976, an arsonist lit a fire on a subway train at Christie station.

On Sundays, these routes operate through the early morning hours, because the subway starts at 9: 00 a. m. instead of the usual 6: 00 a. m.

On March 30, 1954, after five years of work, the first subway in Canada opened to the public.

On August 11, 1995 at 6: 02 pm, the Russell Hill subway accident occurred as a southbound subway train heading toward Dupont Station crashed under Russell Hill Drive, killing three passengers.