Given a field ordering ≤ as in Def 1, the elements such that x ≥ 0 forms a positive cone of F. Conversely, given a positive cone P of F as in Def 2, one can associate a total ordering ≤< sub > P </ sub > by setting x ≤ y to mean y − x ∈ P. This total ordering ≤< sub > P </ sub > satisfies the properties of Def 1.

Given a set of points in Euclidean space, the first principal component corresponds to a line that passes through the multidimensional mean and minimizes the sum of squares of the distances of the points from the line.

Given local and transient influences on surface height, the values defined below are based on a " general purpose " model, refined as globally precisely as possible within 5 m of reference ellipsoid height, and to within 100 m of mean sea level ( neglecting geoid height ).

Given a total interaction cross section σ ( typically measured in barns ), the mean free path of a prompt neutron is where n is the nuclear number density.

Given the observed percentage difference p − q ( 2 % or 0. 02 ) and the standard error of the difference calculated above (. 03 ), any statistical calculator may be used to calculate the probability that a sample from a normal distribution with mean 0. 02 and standard deviation 0. 03 is greater than 0.

Given an assembly of elements, the number of which decreases ultimately to zero, the mean lifetime,, ( also called simply the lifetime ) is the expected value of the amount of time before an object is removed from the assembly.

Fallacious evaluation: " Given that the counterattacks against Germany occurred only after they had conquered the greatest amount of territory under their control, regression to the mean can explain the retreat of German forces from occupied territories as a purely random fluctuation that would have happened without any intervention on the part of the USSR or the Western Allies.

Given a mean AGB lifetime of one Myr and an outer velocity of, its maximum radius can be estimated to be roughly ( 30 light years ).

Given a uniform distribution of backoff times, the expected backoff time is the mean of the possibilities.

Given that the Kuzyk limit is based directly on quantum mechanics, a breaching of the limit would mean that there are problems with quantum theory.

Given the sample mean () and sample coefficient of variation () the parameters and can be estimated:

Given the distribution of Anglicans, this has tended to mean African mission partners joining Crosslinks.

Given Astaire's obsessive rehearsal habits, this was no mean task.

Given the possibility of underlying dimensions emerging from the scale, it is then the case that the scale is no longer balanced, since all the items primarily capturing authoritarian aggression are pro-trait worded ( higher scores mean more authoritarianism ) and all the items primarily measuring conventionalism are con-trait worded ( higher scores mean less authoritarianism ).

Given the atypical Romanian university admission system ( usually another exam making up for the rest of the process ), these percentages mean even less.

Given a set of parameters θ and an input vector x, the mean of the predicted Poisson distribution, as stated above, is given by

Given the arrival of DVDs etc., it is unlikely that any movie ever made will sell as many tickets as DVS Karna sold over 150 million tickets ( currently higher than the next highest ticket selling 19 movies put together!

The season after Given's arrival saw Blackburn win the Premier League title and Given was unable to oust first-choice goalkeeper and England international Tim Flowers from the team.

Given these statements and the continuous arrival of both Autobot and Decepticon forces on Earth, it is unclear if Cybertron is even populated by its people at this point.

Seen as back-up to first-choice goalkeeper Pavel Srníček after his arrival at Newcastle, and then Shaka Hislop and subsequently Shay Given ; he had loan spells at Bradford City, Gateshead, Stockport County, Hartlepool United and Huddersfield Town before making his first-team debut as a half time substitute against Wimbledon in 1998.

Given two sequentially-adjacent registers R < sub > i </ sub > and R < sub > j </ sub > with clock arrival times at register clock pins as T < sub > Ci </ sub > and T < sub > Cj </ sub > respectively, then clock skew can be defined as:

Given their speed and maneuverability, clippers frequently mounted cannon or carronades and were used for piracy, privateering, smuggling, or interdiction service.

Given limited defense budgets, air forces tended to be conservative in their aircraft purchases, and biplanes remained popular with pilots because of their agility, and remained in service long after they had ceased to be competitive.

Given by the Georgia Historical Society, in conjunction with the Governor of Georgia, to individuals whose accomplishments and community service reflect the ideals of the founding body of Trustees, which governed the Georgia colony from 1732 to 1752.

Given the growth of the town of Oxnard, in the spring of 1898, a railroad station was built to service the plant, which attracted a population of Chinese, Japanese, and Mexican laborers and enough commerce to merit the designation of a town.

Given the guaranteed low prices during contract days and the continued high cost of logging in Southeast Alaska today, one analysis concludes that, since 1980, the forest service has lost over a billion dollars in Tongass timber sales.

** Given various time horizons, standards of service, environmental impacts, and conflicts with existing structures or terrain, propose various preliminary designs

Given by the Georgia Historical Society, in conjunction with the Governor of Georgia, to individuals whose accomplishments and community service reflect the ideals of the founding body of Trustees, which governed the Georgia colony from 1732 to 1752.

Given his military service, the selection of Arthur proved to be prudent, as he acted as the King's, and thus the Canadian Commander-in-Chief's, representative through the first years of World War I.

Heterogeneity / Variability: Given the very nature of services, each service offering is unique and cannot be exactly repeated even by the same service provider.

Given by the Georgia Historical Society, in conjunction with the Governor of Georgia, to individuals whose accomplishments and community service reflect the ideals of the founding body of Trustees, which governed the Georgia colony from 1732 to 1752.

Given the problems he was inheriting from Royal Governor Thomas Hutchinson, within a week of arriving Gage contacted Trumbull and expressed a " readiness to cooperate " with him " for the good of his Majesty's service.

Given the predominantly French-speaking population, only CBC, the English-language television service funded by the government of Canada, is available over the air throughout the province.

* Given its URL, the attributes of a service can be requested.

Given their small size the service is very personal, and interaction with the ship's officers is easy.

Given the problems in service and the better lift from the larger wings, blown flaps have generally disappeared.

Given the nature of their creation they are also often in the service of some demon lord or god of evil.

Given the microcosm complex that CIA service tends to cultivate and develop within the organization's comparatively small ranks in combination with the military background of such a large contingency of the agency's active members ; receipt of either of these awards is viewed with utmost admiration almost universally across the " family " of US intelligence services.

Given the opportunity for accelerating services provided by the opening of the Greenisland Loop Lines and the availability of the new powerful Class W 2-6-0 locomotives, a new express service known as the " North Atlantic Express " was introduced between Portrush on the north coast of County Antrim and Belfast.

Given the ability to geocode street addresses and other features, one can create a lot of interesting spatial analysis, location-based service, political campaigning apps and localised search services.

Given that many cases of Sertoli-Leydig cell tumor of the ovary are hereditary, referral to a clinical genetics service should be considered.

* Hillary Clinton: Given on February 18, 2009, for her service to her country and her historic run at the presidency.

Given his devotion and long service to the club, he was subsequently given a place coaching its youth teams.

Order of the Argent Rose of the Outlands ( CARO ): Given for excellence in service to gentles 15 years of age or younger