Given this popular understanding of the term, it can also be used illegitimately and inappropriately, as a means to dismiss what are in fact substantial and well-evidenced accusations.

Given that the vast majority of all emeralds are treated as described above, and the fact that two stones that appear visually similar may actually be quite far apart in treatment level and therefore in value, a consumer considering a purchase of an expensive emerald is well advised to insist upon a treatment report from a reputable gemological laboratory.

Given the first four rolls turn up heads, the probability that the next toss is a head is in fact,

Given its limitations, however, NAALC has not produced ( and in fact was not intended to achieve ) convergence in employment, productivity and salary trend in North America.

Given infinite space, there would, in fact, be an infinite number of Hubble volumes identical to ours in the universe.

Given the above fact, one can ask:

Given that assumption, the evidence for the one-seed theory is the fact that a woman can conceive without coming to orgasm ( though this was still a matter of dispute in the ancient world and the Middle Ages ).

Given the fact that many of the royal depictions of Akhenaten often featured such an elongated head, it is likely an exaggeration of a family trait, rather than a distinct abnormality.

Given any vector space V over K we can construct the tensor algebra T ( V ) of V. The tensor algebra is characterized by the fact:

Given the symmetry of circularly polarized light, we could have in fact selected any other two orthogonal components and found the same phase relationship between them.

" Given the fact that it's the third film in the series, you couldn't just end with them obtaining the object.

Given Switzerland's particularly strong opinions on who is " Swiss " and who is " other ", it is easy to see that groups such as Stoffunita make use of the fact that hip hop " is still considered a voice for the oppressed " as hip hop scholar and author Jeff Chang notes.

Given on 16 October 1732, they amounted only to recreating his first expedition, but with the added task of heading east and finding North America ( a feat which had in fact just been completed by Mikhail Gvozdev, though this was not known at the time ).

Given parallel morphisms f and g, the equaliser of f and g is just the kernel of g − f, if either exists, and the analogous fact is true for coequalisers.

Given the fact that it was an election year, whose outcome might have changed as a result of a pre-election-day economic downturn, the Bank of Mexico decided to buy Mexican Treasury Securities in order to maintain the monetary base, and thus prevent the interest rates from rising.

Given the fact that the Lakeport area has an economy that is based somewhat on agricultural activities occurring in the Big Valley and Scotts Valley area which involve the growing and harvesting of food and nut crops as well as the increasing wine industry, there are a significant number of transient and seasonal farm workers.

Given the extent and central location of his original holding from the Mill Seat Tract, and the fact that most of the town's pre-1944 building lots are to, Bare's ability to shape the size and extent of development in Roaring Spring was substantial.

Given the fact that the following Popes John, from John XV ( 985 – 996 ) until John XIX ( 1024 – 1034 ), seemed to have neglected the existence of John XIV " bis ", Petrus Hispanus meant to correct this error by electing for himself the name John XXI.

Dr. Tennison states: " Given the account of Elliot Paul, and given that Lead Belly witnessed boogie-woogie in 1899 in the Arklatex ; and given the North to South migration of the Thomas family ; and given the Texas & Pacific headquarters in Marshall in the early 1870s ; and given that Harrison County had the largest slave population in the state of Texas ; and given the fact that the best-documented and largest-scale turpentine camps in Texas did not occur until after 1900 in Southeast Texas, it is most probable that boogie-woogie spread from Northeast to Southeast Texas, rather than from Southeast to Northeast Texas, or by having developed diffusely with an even density over all of the Piney Woods of East Texas.

Given the character's unprecedented popularity and the fact that his name was partially derived from the Latin word for " lucky ", some rather notable individuals and organizations adopted Felix as a mascot.

Given the morphological distinctness of the Cape Verde birds and the fact that the Cape Verde population was isolated from other populations of Red Kites, it cannot be conclusively resolved at this time whether the Cape Verde population was not a distinct subspecies ( as M. migrans fasciicauda ) or even species that frequently absorbed stragglers from the migrating European populations into its gene pool.

Given Juwayni's polemical aims, and the fact that he burned the Ismaili libraries which may have offered much more reliable testimony about the history, scholars have been dubious about his narrative but are forced to rely on it given the absence of alternative sources.

Given the epidemic proportions of obesity in the Western world, and the fact that it is increasing rapidly in some poorer countries, observers expect developments in this area to snowball in the near future.

Given the fact that Puerto Rico has 78 municipalities, there was enough material to show and research over the program's six-year run.

While tests have been done to support this with fixed pieces of flat metal, the result is inconclusive with respect to the curved armour of the period. Given the following actions of the archers, it seems likely Froissart was correct.

Given the ( period, cash flow ) pairs (, ) where is the total number of periods, the net present value is given by:

Given the ( period, cash flow ) pairs (, ) where is a positive integer, the total number of periods, and the net present value, the internal rate of return is given by in:

Given that Victoria's finances were in billions of dollars of debt, Kennett was seen from the beginning of his second leadership period as ' Premier-in-waiting '.

Given an eclipse, then there is likely to be another eclipse after every period P. This remains true for a limited time, because the relation is only approximate.

Given Zelazny's academic interest in the Medieval European period, it is not a stretch to see a possible influence in Henry Adams ' 1905 work Mont Saint-Michel and Chartres, wherein he discusses the building of Chartres Cathedral, and the tidal-islet of Mont Saint-Michel, on the Normandy coast of France.

Given the time period when he was alive, Adelard ’ s biography is spotty in places and leaves some aspects open to interpretation.

Given the extremely distorted shape of the primary, the relative orbital motion may be notably altered with respect to the two-body purely Keplerian scenario because of non-negligible long-term orbital perturbations affecting, for example, its orbital period.

Given the financial situation during this period, over-production had to be avoided and thus the notion of Pull ( build to order rather than target driven Push ) came to underpin production scheduling.

Given the concentration of most of this rainfall in the 4 months of Monsoon period, excess rain can lead to floods and shortage to droughts.

Given the difficulty of distinguishing these differences, an accurate and reliable schizoaffective disorder diagnosis usually requires an extended period of observation and treatment.

Given that the high latitudes in this period were warm and tropical, it is hypothesized that the deciduous habit evolved in response to the unusual light availability patterns, not to major seasonal variations in temperature.

* Not being automatically granted the luxury of a “ diagnostic period .” Given that they know the company, COO ’ s turned CEO ’ s are often expected to hit the ground running when in actuality they too need to enter diagnostic mode to fully understand their new role and to see the Company from a new perspective.

Given the price of RAM during the period, up to several hundred dollars per MiB, and the quality and reputation of the above brand names, an expanded memory board was very expensive.

Given the time that is needed to build a new stadium, in the absence of significant work improving Windsor Park, Northern Ireland may be forced to play their home games at a venue outside Northern Ireland for a period.

Given Encke's low orbital inclination near the ecliptic and brief orbital period of 3 years, the orbit of Encke is frequently perturbed by the inner planets.

Given what is known of the chronology of the ‘ Gallic Empire ’ his bid for Empire is most probably associated with the period of confusion following the officers ’ coup against the ‘ Gallic Emperor ’, Victorinus, early in 271.

Given the extended period of time since the war, the Cursed Earth is presumably in the midst of a ( very ) slow environmental recovery with a desert-like environment.

Given the difficult economic circumstances of the Soviet peasantry in the late 1920s and 1930s, chastushki overwhelmingly took an anti-government form, with the singing of anti-Soviet couplets a common practice at peasant festivals of the period.

Given that average yearly temperatures are currently increasing, and the outlook is for this trend to continue, it is actually possible that the glacier might experience a period of stabilization or slight advance during its retreating march.

Given that we know today that the North Pole was covered with thick ice for much of the period, the idea of the Open Polar Sea seems patently ridiculous.

Given that the return period of an event is 50 years,

The optimization attempts to answer the question: " Given our operating constraints, what is the best mix of products and / or services for us to produce and sell in the period, and at what prices, to generate the highest expected revenue?

Given Hollywood's reluctance to hire Asian actors for substantial roles during that period ( with only a few reluctant exceptions, such as Anna May Wong, Sessue Hayakawa, and Philip Ahn ), he portrayed a variety of Asian characters in several movies before being offered the leading role in the 1929 film, The Mysterious Dr. Fu Manchu as the first onscreen portrayal of the title character.