Under the assumption of the generalized Riemann hypothesis, it can be shown to take time

Under the Riemann hypothesis, the zeros of the eta function would be located symmetrically with respect to the real axis on two parallel lines, and on the perpendicular half line formed by the negative real axis.

Under the name Riemann's existence theorem a deeper result on ramified coverings of a compact Riemann surface was known: such finite coverings as topological spaces are classified by permutation representations of the fundamental group of the complement of the ramification points.

Under the null hypothesis of no autocorrelation, this statistic is

Under null hypothesis that the sample comes from the hypothesized distribution F ( x ),

Under a stronger hypothesis they showed that for infinitely many n at least two of n, n + 2, n + 4, and n + 6 are prime.

Under the Kurgan hypothesis, there are two possibilities for how the early Anatolian speakers could have reached Anatolia: from the north via the Caucasus, and from the west, via the Balkans, the latter of which is considered somewhat more likely by Mallory ( 1989 ) and Steiner ( 1990 ).

Under the contact hypothesis, several models have been developed.

Under this null hypothesis, the data are considered unlikely ( with a fair coin, the probability of this is 3 % and the result would be even more unlikely if the coin were biased in favour of tails ).

Under the null hypothesis that model 2 does not provide a significantly better fit than model 1, F will have an F distribution, with ( p < sub > 2 </ sub > − p < sub > 1 </ sub >, n − p < sub > 2 </ sub >) degrees of freedom.

Under the umbrella of the Plate hypothesis, the following sub-processes, all of which can contribute to permitting surface volcanism, are recognised:

Under this alternative hypothesis the disks and arms are modified version of the original stellar disk of the transformed spiral galaxy, and similarly, small remnants of disks and arms are embedded within " harassed " dEs.

# Under the null hypothesis the distributions of both groups are equal, so that the probability of an observation from one population ( X ) exceeding an observation from the second population ( Y ) equals the probability of an observation from Y exceeding an observation from X, that is, there is a symmetry between populations with respect to probability of random drawing of a larger observation.

# Under the alternative hypothesis the probability of an observation from one population ( X ) exceeding an observation from the second population ( Y ) ( after exclusion of ties ) is not equal to 0. 5.

Under this hypothesis, separate parts of reality would have wildly different characteristics.

Under the Mandibulata hypothesis, Myriapoda is the sister taxon to Pancrustacea, a group comprising the Crustacea and Hexapoda.

Under the Atelocerata hypothesis, Hexapoda is the closest, whereas under the Paradoxopoda hypothesis, Chelicerata is the closest.

Under the further assumption that the population error term is normally distributed, the researcher can use these estimated standard errors to create confidence intervals and conduct hypothesis tests about the population parameters.

Under the " packed planetary systems " hypothesis, which predicts that planetary systems form in such a way that the system could not support additional planets between the orbits of the existing ones, the gap would be expected to host a planet.

Under this hypothesis, both male and female Neanderthals participated in the single main occupation of hunting big game that flourished in Europe in the ice age like bison, deer, gazelles and wild horses.

Under the null hypothesis the expected distance ( r < sub > e </ sub > ) between the organisms ( measured as the nearest neighbour's distance ) with a known constant density ( ρ ) is

Under the null hypothesis of no difference between population means ( and assuming that standard ANOVA regularity assumptions are satisfied ) the sums of squares have scaled chi-squared distributions, with the corresponding degrees of freedom.

Under such an hypothesis, the aether should have been observed.

Under this interpretation, the physical symbol system hypothesis asserts merely that intelligence can be digitized.

Under § 216 ( d ) of the Interstate Commerce Act, which forbids any interstate common carrier by motor vehicle to subject any person to unjust discrimination, petitioner had a federal right to remain in the white portion of the restaurant, he was there " under authority of law ," and it was error to affirm his conviction.

Once discharge is finalized, General, Entry-Level / Uncharacterized, and Under Other Than Honorable Conditions ( UOTHC or OTH ) discharges may be appealed for upgrade through the Discharge Review Board of the respective service, however, the appeal must be filed within 15 years of the date of separation, and it must be shown that the characterization of service was the result of an error or injustice.

Under normality assumptions about error distributions, the counterpart of the sum of squares due to error has a Wishart distribution.

Under squared error loss ( SEL ), the conditional expectation E ( θ < sub > i </ sub > | Y < sub > i </ sub > = y < sub > i </ sub >) is a reasonable quantity to use for prediction.

Under the assumption that the population error term has a constant variance, the estimate of that variance is given by:

Under this theory the triple-fourteen parallelism was only created after this error appeared.

Under what some say was pressure from the Vatican, he backed the Taif Agreement and hence the Syrian mandate over Lebanon in order to end the civil war, saying that it was " a fatal error to believe that we can live alone on an island in which we run our affairs as we like.

Under Canadian law, the term " Canadian rye whisky " is simply synonymous with " Canadian whisky ", and the primary mash ingredient in most Canadian whisky is corn.

Under common law, a liquidated damages clause will not be enforced if the purpose of the term is solely to punish a breach ( in this case it is termed penal damages ).

Under the influence of English, which uses the preposition " to " for both indirect objects ( give to ) and directions of movement ( go to ), the term " dative " has sometimes been used to describe cases that in other languages would more appropriately be called lative.

Under Mahuad's recession-plagued term, the economy shrank significantly and inflation reached levels of up to 60 percent.

Under the rating system of the Royal Navy, by the middle of the 18th century, the term " frigate " was technically restricted to single-decked ships of the fifth rate, though small 28-gun frigates were classed as sixth rate.

Under the new rules, only those irradiated foods in which the irradiation causes a material change in the food, or a material change in the consequences that may result from the use of the food, would bear the Radura symbol and the term " irradiated ", or a derivative thereof, in conjunction with explicit language describing the change in the food or its conditions of use.

Under the new constitution, Nasir was elected indirectly to a four-year presidential term by the Majlis ( legislature ).

Under the terms of the accord, both sides agreed to disarm, Díaz would be allowed to finish his term and a new national army would be established, the Guardia Nacional ( National Guard ), with U. S. soldiers remaining in the country to supervise the upcoming November presidential election.

Under many philosophical definitions of the term " deity ", senses 2, 3 and 4 can be shown to be equivalent.

Under the World Trade Organization's ( WTO ) Agreement on Trade-Related Aspects of Intellectual Property Rights, patents should be available in WTO member states for any invention, in all fields of technology, and the term of protection available should be a minimum of twenty years.

Skinner put forward a " three term contingency model " which helped promote analysis of behavior based on the " Stimulus-Response-Consequence Model " in which the critical question is: " Under which circumstances or antecedent ' stimuli ' does the organism engage in a particular behavior or ' response ', which in turn produces a particular ' consequence '?

Under the 1963 constitution, Massamba-Débat was elected President for a 5-year term and named Pascal Lissouba to serve as Prime Minister.

Under the Thatcher government 1979 – 90 the term was revived for private ministerial meetings at which disputes between the Treasury and high-spending departments were resolved.

Under the 1992 constitution, the president is elected by popular vote for a five-year term.

Under the 1966 Social Security Act, newly unemployed individuals were no longer denied assistance during their first month of unemployment, while men who had had their unemployment benefit disallowed for six weeks ( on the grounds that they had been at fault for losing their job ) were no longer subjected to a harsh rule applied by the National Assistance confining their payments to below “ benefit rate .” Instead, a policy was adopted of paying these individuals their full entitlement less 15 shillings. T he Act also introduced a long term addition of 9 shillings for all pensioners receiving supplementary benefit and for others ( with the exception of those required register for employment ) receiving supplementary benefits for two years.

Under the influence of this doctrine, and of Phenomenology, the Hungarian-born German sociologist Karl Mannheim ( 1893 – 1947 ) gave impetus to the growth of the sociology of knowledge with his Ideologie und Utopie ( 1929, translated and extended in 1936 as Ideology and Utopia ), although the term had been introduced five years earlier by the co-founder of the movement, the German philosopher, phenomenologist and social theorist Max Scheler ( 1874 – 1928 ), in Versuche zu einer Soziologie des Wissens ( 1924, Attempts at a Sociology of Knowledge ).

The novel is linked to Heinlein's short story, " They ", by the term, " the Glaroon ", and to his earlier novel The Moon is a Harsh Mistress by referring to the Moon colonies " Luna City " and " Tycho Under ".

Under the Basic Law the president was to be elected by a specially convened body called the Federal Convention ( Bundesversammlung ) to serve a five-year term.

Under Leopold I ( 1658 – 1705 ) the term again became Hofkanzler with Johann Paul Freiherr von Hocher ( 1667-1683 ), and Theodor von Strattman ( 1683-1693 ).

Under Anderson, Wired has produced some widely noted articles, including the April 2003 " Welcome to the Hydrogen Economy " story, the November 2003 " Open Source Everywhere " issue ( which put Linus Torvalds on the cover and articulated the idea that the open source method was taking off outside of software, including encyclopedias as evidenced by Wikipedia ), the February 2004 " Kiss Your Cubicle Goodbye " issue ( which presented the outsourcing issue from both American and Indian perspectives ), and an October 2004 article by Chris Anderson, which coined the popular term " Long Tail.

# Under some definitions the term adjectival phrase is only used for phrases in attributive position, within the noun phrase they modify.

All activities refer to a time t. Under certain circumstances ( see chemical equilibrium ) each activity term such as may be replaced by a concentration term,.

Under Russia's 1993 constitution, there are 450 deputies of the State Duma ( Article 95 ), each elected to a term of four years ( Article 96 ); this was changed to a five-year term in late 2008.