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Page "Ordered field" ¶ 25
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Since and 1
Since accurate base maps are necessary for any planning program, the first step taken by the planning division to implement the long-range state plan has been to prepare two series of base maps -- one at a scale of 1 inch to a mile, and the second a series of 26 sheets at a scale of 1 inch to 2000 feet, covering the entire state.
Since the provision of skywave service requires adequate freedom from interference, only class 1, stations are capable of rendering skywave service.
Since Parts 1, and 2, were prepared independently, the abbreviation schemes and the chemical symbols used differ in the two parts.
Since we are considering here relatively small diameter ( 1 - 1.5 inches ) fiber plates, their average thickness can be kept below 1/4 inch and their internal losses may be assumed as 15 percent ( per plate ).
Since 1949, the St. Louis club has been below on May 1 just four times.
Since then the corporate headquarters have moved to New York City at 1 Park Avenue in Manhattan.
Since 1 April 1956, Aalen has the status of Große Kreisstadt (“ major district town ”).
This subextension is called a separable closure of K. Since a separable extension of a separable extension is again separable, there are no finite separable extensions of K < sup > sep </ sup >, of degree > 1.
Since the bigger 1 / 4 " tapioca pearls are separately sold as " black pearls " ( 黑珍珠 ) in markets, this name was the logical first choice and is more popular with the consumers of the drink.
Since B < sub > n </ sub >= 0 for all odd n > 1, and many formulas only involve even-index Bernoulli numbers, some authors write B < sub > n </ sub > instead of B < sub > 2n </ sub >.
Since 2003, a 1, 070 km pipeline has been used to export crude oil from the oilfields around Doba to offshore oil-loading facilities on Cameroon's Atlantic coast at Kribi.
Since the U. S .- Chile Free Trade Agreement went into effect on January 1, 2004, U. S .- Chilean trade has increased by 154 %.
Since these stock additions retain the short pistol barrel ( as short as 100 mm ( 4 inches )) they are highly restricted under the NFA unless the shoulder stocks are of original manufacture for the gun and the gun has been " delisted " as outlined in links 1 & 2 in the paragraph above, as is the case with so-equipped " Broomhandle " Mausers and Lugers.
Since then, she has donated over US $ 1 million to the program.
Since a comic book shop in his area traded 2 old comics for 1 new, he only had 2 Duck comics left from his sister's collection by the 70s, one of them being The Golden Helmet.
Since all probabilities p < sub > i </ sub > add up to one: p < sub > 1 </ sub > + p < sub > 2 </ sub > + ... + p < sub > k </ sub > = 1, the expected value can be viewed as the weighted average, with p < sub > i </ sub >’ s being the weights:
Since its unification with Pakistan, the East Pakistan Army had consisted of only one infantry brigade, which was made up of two battalions, the 1st East Bengal Regiment and the 1 / 14 or 3 / 8 Punjab Regiment in 1948.
Since the algorithm ensures that the remainders decrease steadily with every step, r < sub > k − 1 </ sub > is less than its predecessor r < sub > k − 2 </ sub >.
In the first step, the final nonzero remainder r < sub > N − 1 </ sub > is shown to divide both a and b. Since it is a common divisor, it must be less than or equal to the greatest common divisor g. In the second step, it is shown that any common divisor of a and b, including g, must divide r < sub > N − 1 </ sub >; therefore, g must be less than or equal to r < sub > N − 1 </ sub >.
Since r < sub > N − 1 </ sub > is a common divisor of a and b, r < sub > N − 1 </ sub > ≤ g.

Since and >
Since 1983 ,< ref >
Since n grows faster than log < sub > 2 </ sub >( n ), there must exist a value n < sub > 0 </ sub > such that
Since the 1990s, SO < sub > 2 </ sub > emissions have dropped 40 %, and according to the Pacific Research Institute, acid rain levels have dropped 65 % since 1976.
During a 1935 – 1942 colonization attempt, the island was most likely on Hawaii time, which was then 10. 5 hours behind UTC .< ref > Since it is uninhabited the island's time zone is unspecified, but it lies within a nautical time zone 12 hours behind UTC.
Since the 2002 civil war in Côte d ' Ivoire, relations between it and Burkina Faso have been filled with accusations of Burkinabé support for rebels on one side and claims of mistreatment of Burkinabé workers on the other .< ref > Blaise Campaoré :<< La crise ivoirienne inquiète le Burkina >>, Le Figaro, December 11, 2005 </ ref > Côte d ' Ivoire remains Burkina Faso's largest regional trading partner in spite of their disputes and tens of thousands of Burkinabés continue to work in the Ivory Coast.
Since the mass numbers of these are 12, 13 and 14 respectively, the three isotopes of carbon are known as carbon-12, carbon-13, and carbon-14, often abbreviated to < sup > 12 </ sup > C, < sup > 13 </ sup > C, and < sup > 14 </ sup > C.
Since the map d restricts to 0 on I < sub > x </ sub >< sup > 2 </ sup > ( the reader should verify this ), d descends to a map from I < sub > x </ sub > / I < sub > x </ sub >< sup > 2 </ sup > to the dual of the tangent space, ( T < sub > x </ sub > M )< sup >*</ sup >.

Since and 0
Since the difference between the U. S. and International acre is only about a quarter of the size of an A4 sheet of paper ( 0. 016 square metres, 160 square centimetres or 24. 8 square inches ), it is usually not important which one is being discussed.
A set S is called countable if there exists an injective function f from S to the natural numbers Since there is an obvious bijection between and it makes no difference whether one considers 0 to be a natural number of not.
Since the separation of variables in this case involves dividing by y, we must check if the constant function y = 0 is a solution of the original equation.
Since 1993, the Eritrean People ’ s Liberation Front army has been involved in tree planting ; the annual average rate of deforestation during 1990 – 2000 was 0. 3 percent.
Since the release of EDIF 4 0 0, the entire EDIF standards organisation has essentially dissolved.
The event temporarily warmed air temperature by 1. 5 ° C, compared to the usual increase of 0. 25 ° C associated with El Niño events .< ref name =" Trenberth "> Since then, mass coral bleaching has become common worldwide, with all regions having suffered " severe bleaching ".
Since the Tigers " ran up a 61 to 0 score on the hapless Mountain Staters, the pass played no important part in the result.
Since Version 0. 7 ( 2008 ), it offers two modes of operation: a darknet mode in which it connects only to friends, and an opennet-mode in which it connects to any other Freenet user.
Since Version 0. 7, Freenet offers two different levels of security: Opennet and Darknet.
Since version 0. 6, gnutella is a composite network made of leaf nodes and ultra nodes ( also called ultrapeers ).
Since version 7. 0, support for " reversible debugging " — allowing a debugging session to step backward, much like rewinding a crashed program to see what happened — is available.
Since 1995, Hungary has pegged the forint against a basket of currencies ( in which the U. S. dollar is 30 %), and the central rate against the basket is devalued at a preannounced rate, originally set at 0. 8 % per month, the Forint is now an entirely free-floating currency.
Since 2004, the alcohol content of Kahlúa is 20. 0 % ( 21. 5 % alc.
Since metallic radii are always biggest for the highest coordination number, correction for less dense coordinations involves dividing by x, where 0 < x < 1.
Since a proportion must be between 0 and 1, inclusive, the index α must be positive, but in order for the total income of the whole population to be finite, α must also be greater than 1.
Since Lowell astronomers thought Pluto was massive enough to perturb planets, they assumed that it should have an albedo of 0. 07 ( meaning that it reflected only 7 % of the light that hit it ); about as dark as asphalt and similar to that of Mercury, the least reflective planet known.
Since J2SE5. 0, Java's library contains a interface that specifies queue operations ; implementing classes include and ( since J2SE 1. 6 ).
Since an event of probability 0 should not contribute to the entropy, and given that, the convention is adopted that.

0.534 seconds.