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 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 September 11, 2008, a United States Air Force C-17 Globemaster III successfully completed the first landing in Antarctica using night-vision goggles at Pegasus Field.

On November 6, 1827, Alcott started teaching in Bristol, Connecticut, still using the same methods he used in Cheshire, but opposition from the community surfaced quickly ; he was unemployed by March 1828.

On occasion, even the soldiers of national militaries are forced to adapt their civilian-type vehicles for combat use, often using improvised armor and scrounged weapons.

The theology of the creed is firmly rooted in the Augustinian tradition, using exact terminology of Augustine's On the Trinity ( published 415 AD ).

On August 19, 1727, Bradley then embarked upon a further series of observations using a telescope of his own erected at the Rectory, Wanstead.

Image showing shock waves from NASA's X-43A hypersonic research vehicle in flight at Mach 7, generated using a computational fluid dynamics algorithm. On September 30, 1935 an exclusive conference was held in Rome with the topic of high velocity flight and the possibility of breaking the sound barrier.

* 2007: On September 16, 2007, hunter Rick Jacobs captured an image of a supposed Sasquatch by using an automatically triggered camera attached to a tree, prompting a spokesperson for the Pennsylvania Game Commission to say that it was likely an image of " a bear with a severe case of mange.

On the other hand, Mac OS X has since version 10. 6 shown hard drive size using decimal prefixes ( thus matching the drive makers ' packaging ).

On 1 September, the pursuing Royalists captured Castle Dore, another ruined fortification which the Parliamentarians were using to anchor their lines.

On that Mississippi riverine system today, including that of other sheltered waterways, industrial barge trafficking in bulk raw materials such as coal, coke, timber, iron ore and other minerals is extremely common in the developed world using huge cargo barges that connect in groups and trains-of-barges in ways which allow cargo volumes and weights which would astonish pioneers of modern barge systems and methods in the Victorian era.

On the other hand, supervisory restructuring at the behest of the Board of Industrial and Financial Reconstruction is generally undertaken using receivership by a Public Finance Institution.

On human nature, Boethius says that humans are essentially good and only when they give in to “ wickedness ” do they “ sink to the level of being an animal .” On justice, he says criminals are not to be abused, rather treated with sympathy and respect, using the analogy of doctor and patient to illustrate the ideal relationship between prosecutor and criminal.

On June 28, 1984 Compaq released the Compaq Deskpro, a 16-bit desktop computer using an Intel 8086 microprocessor running at 7. 14 MHz.

On 22 March 1965, DEC introduced the PDP-8, which replaced the PDP-5's modules with the new R-series modules using Flip Chips.

Some tracks were composed using Eno and Peter Schmidt's Oblique Strategies cards: " Boys Keep Swinging " entailed band members swapping instruments, " Move On " used the chords from Bowie's early composition " All the Young Dudes " played backwards, and " Red Money " took backing tracks from " Sister Midnight ", a piece previously composed with Iggy Pop.

On 27 January 2011 a memorial and museum dedicated to the Holocaust victims killed using Topf ovens was opened at the former company premises in Erfurt.

On 6 August 2010, Trenitalia announced its desire to eventually run high-speed trains from Italy to the United Kingdom, using its newly ordered high-speed trains.

On April 27, 1894, he established communications between the Paris stock exchange and the Milan stock exchange, again over a single wire, using his new invention, the retransmitter.

On June 19, 1872, under the sponsorship of Leland Stanford, Eadweard Muybridge successfully photographed a horse named " Sallie Gardner " in fast motion using a series of 24 stereoscopic cameras.

On the surface, an inventor named Goro Ibuki, his nephew Rokuro and their friend Hiroshi Jinkawa are off on an outing near a lake when Seatopia makes itself known to the Earth by drying up the lake the trio was relaxing nearby and using it as a base of operation ( unknown to our heroes.

The interrelationships between volume change behavior ( dilation, contraction, and consolidation ) and shearing behavior were all connected via the theory of plasticity using critical state soil mechanics by Roscoe, Schofield, and Wroth with the publication of " On the Yielding of Soils " in 1958.

On September 8, 2007, five members of the Makah tribe shot a gray whale using high powered rifles in spite of the decision.