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 expectations about returns on fixed investment, every level of the real interest rate ( i ) will generate a certain level of planned fixed investment and other interest-sensitive spending: lower interest rates encourage higher fixed investment and the like.

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 confidence level, the VaR of the portfolio at the confidence level is given by the smallest number such that the probability that the loss exceeds is at most.

Given the high level of support within the party for her leadership, MacPhail surprised many by choosing not to seek the party leadership in 2003.

Given that the level of hyperforin was not ascertained at the beginning of the study, and levels of both hyperforin and hypericin were well below that used in other studies, little can be determined based on this study alone.

Given the publicly stated protection level for the earliest M1: 350 mm steel equivalence against KE-penetrators ( APFSDS ), it seems to have been equipped with alumina tiles.

Given the weak level of basketball in the Virgin Islands, Odom was wary about Duncan at first, especially after first meeting him and thinking him to be inattentive ; Duncan stared blankly at Odom for most of the conversation.

Given this outlook, whatever the level of affection Whistler may have felt for his own mother, one finds an even more divergent use of the image in the Victorian era and later, especially in the United States, as an icon for motherhood, affection for parents, and " family values " in general.

Given its production function and cost structure, it knows its average total costs at that output level will be represented as point A.

Given figures ranged from, but it is now generally accepted that the peak is above sea level as a result of a survey carried out by the Bavarian State Survey Office.

Given the need for such warheads to reenter the atmosphere swiftly and retain hypersonic velocities to sea level, researchers developed what are known as SHARP materials, typically hafnium diboride and zirconium diboride, whose thermal tolerance exceeds 3600 C. SHARP equipped vehicles can fly at Mach 11 at 30 km altitude and Mach 7 at sea level.

Given the level of business can vary week to week, it is not uncommon for escorts to be featured by more than one agency provided they are operated by the same ownership group.

Given that the Oostvaardersplassen is below sea level, many of its primary processes have been regulated.

Given the increasing role of the European Union in the political arena, the National Academies acknowledge that the scope of their advisory tasks must exceed the national borders and that it's important not to lose sight of the European level.

Given the overall low level of water tariffs in developing countries even at higher levels of consumption, most consumption subsidies benefit the wealthier segments of society.

Given the variable half-life of flecainide and the characteristic QRS prolongation on ECG elicited in flecainide toxicity, especially at rapid heart rates, starting flecainide or changing the level of the drug is done under telemetry monitoring ( preferably in a hospital telemetry unit ) until a steady state plasma level has been achieved, typically three to five days after the dose has been increased.

Given a connected graph G =( V, E ) with V the set of vertices and E the set of edges, and with a root vertex r, the level structure is a partition of the vertices into subsets L < sub > i </ sub > called levels, consisting of the vertices at distance i from r. Equivalently, this set may be defined by setting L < sub > 0 </ sub > =

Given that the then government of the day, had refused to allow BR to purchase more DEMUs in the mid 1960s, this led to problems of trying to run existing services with a significantly reduced level of motive power available following the total withdrawal of steam in 1967.

Given a square of 2 < sup > 2k </ sup > cells, 2 < sup > k </ sup > on a side, at the kth level of the tree, the hash table stores the 2 < sup > k-1 </ sup >- by-2 < sup > k-1 </ sup > square of cells in the center, 2 < sup > k-2 </ sup > generations in the future.

Given the scope of modern regulation, however, legislatures frequently find areas where it is impractical for lawmakers to apply the level of detail or expertise required to establish complete standards.

Given the long surveillance hours, Morrison feels the odds are against him to smoke on the sly.

Given my tiny force of eighty-one observers and the fact that we had no helicopters with night-vision capability, the task of keeping the border under surveillance was at best symbolic.

* U. S. surveillance: the Los Angeles Times reported on 27 October 2004: " Given the size of the missing cache, it would have been difficult to relocate undetected before the invasion, when U. S. spy satellites were monitoring activity.

Given that Communist Romania was a police state, and unprecedented measures of strict control and surveillance were supposed to have been enforced in all areas of society ( phone calls were routinely monitored, correspondence was intercepted, and secret police informants were common ) a plan such as the one allegedly designed by the group would have been exceedingly difficult to carry out.

Given a sample of wood, the variation of the tree ring growths provides not only a match by year, it can also match location because the climate across a continent is not consistent.

Given the consistent failures in this research literature to disprove the null hypothesis, the burden of empirical proof is on those who argue that the children of sexual minority parents are worse off than the children of heterosexual parents.

The general scenario is the following: Given a class S of computable functions, is there a learner ( that is, recursive functional ) which for any input of the form ( f ( 0 ), f ( 1 ),..., f ( n )) outputs a hypothesis ( an index e with respect to a previously agreed on acceptable numbering of all computable functions ; the indexed function should be consistent with the given values of f ).

Given the Northwest Region ’ s rich heritage for foreign missions, such a vision is deeply consistent with our ethos and tradition .”

Given that the relevant cardinals exist, it is consistent with ZFC either that the first measurable cardinal is strongly compact, or that the first strongly compact cardinal is supercompact ; these cannot both be true, however.

Given with appropriate resources ; the MDRRC is tasked to approve, monitor and evaluate the implementation of MDRRC plans and review, test and develop the plan consistent with other national and local planning programs.

Given that the colocynth grows wild in region of Israel, these symptoms would be consistent with the " wild gourd " mentioned in 2 Kings 4: 39-40.

: Given any set X of pairwise disjoint non-empty sets, there exists at least one set C that contains exactly one element in common with each of the sets in X.

* Given an algebraic number, there is a unique monic polynomial ( with rational coefficients ) of least degree that has the number as a root.

Given two subspaces with, this leads to a definition of angles called canonical or principal angles between subspaces.

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 this influence, it is unfortunate that many of the details of his life remain shrouded in mystery, perhaps forever ; even the only known picture of him, shown above, is heavily retouched, with a fake tie painted in by hand.

Given the opportunity, adults eat hatchlings, which may be protected by separating the two groups with a net, breeding box or separate tank.

Love and Erlandson continued to pursue with the band, and released the single " Be A Man "— an outtake from the Celebrity Skin sessions — for the soundtrack of the Oliver Stone film Any Given Sunday ( 1999 ).

Given that many journeys are for relatively short distances, there is considerable scope to replace car use with walking or cycling, though in many settings this may require some infrastructure modification, particularly to attract the less experienced and confident.

Given an asymmetric subunit on a triangular face of a regular isosahedron, with three subunits per face 60 such subunits can be placed in an equivalent manner.

Given the bias of the Victorian age, female students were denied direct study in anatomy and could not attend drawing classes with live models ( who were often prostitutes ) until a decade later.

Given the small population of the region ( compared with the Central Canadian provinces or the New England states ), the regional economy is a net exporter of natural resources, manufactured goods, and services.

Given the rigorous admission process it is not surprising that CUNY BA boasts a 70 % graduation rate within an average of 2. 2 years and that 60 % graduate with academic honors.

Given Chrétien's known tendency to create new stories and characters, being the first to mention the hero Lancelot and his love affair with Queen Guinevere for example, the name might also be entirely invented.

Given that the dispute with Pizarro over Cuzco had kept intensifying, Almagro spent a great deal of time and money equipping a company of 500 men for a new exploration south of Peru.

Given Mountbatten's determination, Nehru and Patel's inability to deal with the Muslim League and lastly Jinnah's obstinacy, all Indian party leaders ( except Gandhi ) acquiesced to Jinnah's plan to divide India, which in turn eased Mountbatten's task.

Given this kind of data, the estimated coefficient on Years of Education in the equation above reflects both the effect of education on wages and the effect of other variables on wages, if those other variables were correlated with education.

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 Guatemala's large expatriate community in the United States, it is the top remittance recipient in Central America, with inflows serving as a primary source of foreign income equivalent to nearly two-thirds of exports.

Given a trigonometric series f ( x ) with S as its set of zeros, Cantor had discovered a procedure that produced another trigonometric series that had S ' as its set of zeros, where S ' is the set of limit points of S. If p ( 1 ) is the set of limit points of S, then he could construct a trigonometric series whose zeros are p ( 1 ).

Given that Gable and Cukor had worked together before, in Manhattan Melodrama and Gable had no objection to working with him then, and given Selznick's desperation to get Gable for Rhett Butler, if Gable had any objections to Cukor, certainly they would have been expressed before he signed his contract for the film.

Given the differences of opinion within the Lord Aberdeen cabinet over the direction of foreign policy with regard to relations between Britain and the French under Napoleon III, it is not surprising that debate raged within the government as Louis Bonaparte, now assuming the title of Emperor Napoleon III of France.

Given a finite dimensional real quadratic space with quadratic form, the geometric algebra for this quadratic space is the Clifford algebra Cℓ ( V, Q ).

Given the limited amount of good quality agricultural land to begin with, that policy has resulted in continual deforestation and subsequent erosion.

On poverty, Hoover said that " Given the chance to go forward with the policies of the last eight years, we shall soon with the help of God, be in sight of the day when poverty will be banished from this nation ", and promised, " We in America today are nearer to the final triumph over poverty than ever before in the history of any land ," but within months, the Stock Market Crash of 1929 occurred, and the world's economy spiraled downward into the Great Depression.