Two natural numbers a and b are coprime if and only if the numbers 2 < sup > a </ sup > − 1 and 2 < sup > b </ sup > − 1 are coprime.

Two natural " safe " directions to point the muzzle are upwards ( at the sky ) and downwards ( at the ground ).

John Locke incorporated natural law into many of his theories and philosophy, especially in Two Treatises of Government.

where n is a natural number, the coefficients are elements of R, and X is a formal symbol, whose powers X < sup > i </ sup > are just placeholders for the corresponding coefficients a < sub > i </ sub >, so that the given formal expression is just a way to encode the sequence, where there is an n such that a < sub > i </ sub > = 0 for all i > n. Two polynomials sharing the same value of n are considered equal if and only if the sequences of their coefficients are equal ; furthermore any polynomial is equal to any polynomial with greater value of n obtained from it by adding terms in front whose coefficient is zero.

Two exceptions to standard poker practice sometimes seen in home games are the double-ace flush rule, and the natural wins rule.

Two natural gas lines parallel the old petroleum line as far as Tbilisi, where they turn north across the Caucasus Mountains to join the grid of natural gas pipelines that supply cities throughout Russia and Eastern Europe.

Two similar concepts in contemporary English law are natural justice ( which generally applies only to decisions of administrative agencies and some types of private bodies like trade unions ) and the British constitutional concept of the rule of law as articulated by A. V. Dicey and others.

Two functors F and G are called naturally isomorphic or simply isomorphic if there exists a natural isomorphism from F to G.

In his analysis of medieval political theology, The King ’ s Two Bodies, Ernst Kantorowicz describes medieval Kings as containing two bodies: a body natural, and a body politic.

Locke argued in Two Treatises of Government that the individual placed some of his rights present in the state of nature in trusteeship with the sovereign ( government ) in return for protection of certain natural individual rights.

However, the Great Depression, a post-World War Two switch to mostly natural gas and electric heat in American homes, and heavy industry ’ s lessening coal use doomed the area coal fields.

Two independent variants of the APOL1 gene found in African haplotypes carrying signatures of natural selection have been shown to confer protection against the acute version of sleeping sickness caused by T. b. rhodesiense, while at the same time increasing risk of kidney disease when inherited from both parents.

Two local organizations: the German-American Mutual Assistance Foundation, to insure residents against natural disasters ; and " Pflugerville Schuetzen and Kegel Verein ," a shooting and bowling club.

Two main varieties of speech recognition are used in IVR: that based upon predefined grammars ( used in " directed " dialogues ), and that based on statistically trained language models ( used in " natural language " dialogues ).

Two cast members died within two months of each other in 1998: Mary Millar, who played Rose from 1991 to 1995, on 10 November 1998 due to ovarian cancer ; and George Webb, who played Daddy throughout the show's run, on 30 December 1998, of natural causes.

Two natural areas: the iSimangaliso Wetland Park and the uKhahlamba Drakensberg Park, have been declared UNESCO World Heritage Sites.

Two years later, in the summer of 2008, another natural disaster struck the campus.

This made him a natural born citizen of the United States under the Articles of Confederation and as defined in Section 1 of Article Two of the United States Constitution.

* Two examples of natural beauty: the Fisherman Momerioland the Sreburna Nature Reserve

Two SD-40 diesel-electric locomotives fuelled with 90 % natural gas and 10 % diesel are in service between Edmonton and Fort McMurray, Alberta ..

Two Canadian studies, that received funding by the Alberta Livestock and Meat Agency and the Dairy Farmers of Canada, have shown that the natural trans fat vaccenic acid, found in beef and dairy products, may have an opposite health effect and could actually be beneficial compared to hydrogenated vegetable shortening, or a mixture of pork lard and soy fat, e. g. lowering total and LDL cholesterol and triglyceride levels.

Two major river systems, the Abulog and the Apayao, run through Isneg country, which until recent times has been described as a region of “ dark tropical forests ,” and endowed with other natural resources.

Two vector spaces over the same field with the same dimensionality are always isomorphic ; but not necessarily in a natural or canonical way.

Although the concept of consilience in Whewell's sense was widely discussed by philosophers of science, the term was unfamiliar to the broader public until the end of the 20th century, when it was revived in Consilience: The Unity of Knowledge, a 1998 book by the humanist biologist Edward Osborne Wilson, as an attempt to bridge the culture gap between the sciences and the humanities that was the subject of C. P. Snow's The Two Cultures and the Scientific Revolution ( 1959 ).

Two of her philosophical works, Pensées diverses and Considérations générales sur l ' état des sciences et des letteres aux différentes epoques de leur culture, were published, both posthumously.

Subsequently published as The Two Cultures and the Scientific Revolution, the lecture argued that the breakdown of communication between the " two cultures " of modern society – the sciences and the humanities – was a major hindrance to solving the world's problems.

Two courses in humanities, one each in math and science, two in social sciences, two in religious studies, foreign language as needed, and a diversity course are required of almost all students.

* May 7-Scientist and novelist C. P. Snow delivers an influential Rede Lecture on The Two Cultures, concerning a perceived breakdown of communication between the sciences and humanities, in the Senate House, University of Cambridge.

Two years later, he gained a scholarship to King's College, Cambridge, where he graduated with first-class honours in the natural sciences tripos in 1903.

Two further experiments involved atmospheric sciences, while one was in communications research.

Two scientific symposia in the medical sciences took place in 1995 under the auspices of the Polish Academy of Arts and Sciences.

Two academicians, 15 doctors and professors and 33 candidates of sciences are occupied in the educational process at this faculty.

Two prominent libraries, the Harlan Hatcher Graduate Library and the Shapiro Undergraduate Library which are connected by a skywalk, are also on Central Campus, as well as museums housing collections in archaeology, anthropology, paleontology, zoology, dentistry, and art.

Two other museums are on the list, the Art Museum and the Naturmuseum.

Two other museums are in Kanchanaburi: the Thailand-Burma Railway Museum, opened in March 2003, and the JEATH War Museum.

Ashdown has two museums: the Two Rivers Museum and the Hunter / Coulter Museum.

Easton's Two Rivers Landing is the home of two interactive children's museums, the National Canal Museum, which focuses on the importance of canals in the region, and the Crayola Factory, which is owned by Crayola LLC ( formerly known as Binney & Smith ), a major toy manufacturer based in nearby Forks Township.

Two sets of death duties in the 1940s, and the nationalization of their coal mines, greatly reduced the wealth of the Fitzwilliams, and most of the contents of the house were dispersed, in auction sales in 1948, 1986 and 1998, though many remain in the family, with many works loaned to museums by the " Trustees of the Fitzwilliam Estates ".

Two dozen wooden objects bearing rongorongo inscriptions, some heavily weathered, burned, or otherwise damaged, were collected in the late 19th century and are now scattered in museums and private collections.

Two cloisters — one secular, one for the monks — survive as the courtyards of the brick-and-stone 17th-century domestic ranges, now housing the Museum of the Principality of Stavelot-Malmedy, and museums devoted to the poet Guillaume Apollinaire, who was a long-term resident, and to the Circuit de Spa-Francorchamps.

Note: Two stacked Titan-1 first stages created a perfect illusion of a Titan-2 Missile for museums above.

Two major museums in Vienna have branch offices in Leopoldstadt.

Two impressive examples of the military type are housed in the museums of Vienna, both from the sixteenth century.

Two museums are located within the abbey complex, one devoted to the abbey and one to the town.

Two museums, one in Berlin and Cologne, are dedicated solely to her work.

Two museums have been named in Acuff's honor — the Roy Acuff Museum at Opryland and the Roy Acuff Union Museum and Library in his hometown of Maynardville.

* Two museums, the Musée de l ' abri Pataud in Les Eyzies-de-Tayac and the Harmas de Fabre in Sérignan-du-Comtat,

Two museums, the RAF Manston History Museum and the Spitfire and Hurricane memorial, are located on the northern edge of the airfield.

Two German museums Deutsches Panzermuseum at Munster and Wehrtechnische Studiensammlung ( WTS ) at Koblenz have one running Jagdpanther each.

Two museums are also across Juramento and Cuba streets: Larreta and Sarmiento, respectively.

Two Hutsul-related museums are located in Kolomyia, Ukraine: the Pysanky museum and the Museum of Hutsul and Pokuttya Folk Art.

Two of these towers, Murney Tower and Fort Frederick are open to the public and contain museums.

Two 4-4-0 locomotives, The General, and The Texas from the NC & StL's predecessor road, the Western and Atlantic, are on display in museums in the Atlanta suburbs of Kennesaw and Grant Park.

The bulk of their art collection was sold at auction in 1929 Two works once in their collection are in the National Gallery, three at the National Gallery of Art, Washington, and others at the ( Mellon ) Yale Center for British Art and other museums.

Two of the Carnegie museums, the Carnegie Museum of Natural History and the Carnegie Museum of Art, are both located in the Carnegie Institute and Library complex in Oakland, a landmark building listed on the National Register of Historic Places ( ref # 79002158, added 1979 ) that also houses the Carnegie Music Hall and the main branch of the Carnegie Library of Pittsburgh.

Two smaller museums, one containing the presidential memorabilia of Quezon, and the other containing items on the history of Quezon City, were installed within the monument itself.