Under these conditions a new generation of Europeans began to discover the bonds of long association and shared values that for so long had been subordinated to nationalist xenophobia.

Under these schemes, authors are paid a fee for the number of copies of their books in educational and / or public libraries.

Under one of these emperors, Romanos IV Diogenes ( 1067 – 1071 ), Alexios served with distinction against the Seljuq Turks.

Under the strong rule of Abdur Rahman these outlying territories were closely welded to Kabul ; but after the accession of Habibullah the bonds once more relaxed.

Under 10 % of organisms were predators or scavengers, although since these organisms were larger, the biomass was split equally between each of the filter feeding, deposit feeding, predatory and scavenging organisms.

Under these rules, if a man went down and could not continue after a count of 30 seconds, the fight was over.

Under these conditions however, it was difficult for German commanders to employ the “ armoured idea ” to its envisioned potential.

Under these conditions I find it virtually impossible to continue my motion-picture work, and I have therefore given up my residence in the United States.

Under these new policies, the rate of inflation dropped from about 1, 000 % per year to about 10 % per year.

Under exceptional circumstances, a redive may be granted, but these are exceedingly rare ( usually for very young divers just learning how to compete, or if some event outside the diver's control has caused them to be unable to perform ).

Under these conditions, many bacterial cells burst, releasing a pulse of nutrients.

Under this policy, Albania would develop its agricultural output in order to supply the Soviet Union and other Warsaw Pact nations while these nations would be developing specific resource outputs of their own, which would in theory strengthen the Warsaw Pact by greatly reducing the lack of certain resources that many of the nations faced.

Under the terms of the accord, films produced using these funds can only be screened on television 24 months after their theatrical release.

Under the disputed Nostratic theory and similar theories such as that of monogenesis, some of these examples would indeed be distantly related cognates, but the evidence for reclassifying them as such is insufficient.

Under Greek pressure, the European Union and NATO agreed that in order for the Republic of Macedonia to receive an invitation to join these institutions the name dispute must be resolved first.

Under Himmler's orders via the RSHA, these squads were also tasked with rounding up Jews and others for placement in ghettos and concentration camps.

Under the so-called " Volcker Rule ", regulators are also required to implement regulations for banks, their affiliates and holding companies to limit their relationships with hedge funds and also to prohibit these organizations from proprietary trading, and limit their investment in, and sponsorship of hedge funds.

Under these constraints, we would like to maximize the rate of information, or the signal, we can communicate over the channel.

Under this legislation, the federal government paid towards around 50 % of the cost of provincial health plans to cover “ a basic range of inpatient services in acute, convalescent, and chronic hospital care .” The condition for those cost-sharing legislation was that all citizens were to be entitled to these benefits, and by March 1963 98. 8 of Canadians were covered by Hospital Insurance.

" Under the law of association, transmission of wealth does not apply to the instruments of labour, so cannot become a cause of inequality .... We are socialists ... under universal association, ownership of the land and of the instruments of labour is social ownership ... We want the mines, canals, railways handed over to democratically organised workers ' associations ... We want these associations to be models for agriculture, industry and trade, the pioneering core of that vast federation of companies and societies, joined together in the common bond of the democratic and social Republic.

Under these circumstances, during much of the Siege of Leningrad ( 1941 – 1944 ), Lake Ladoga provided the only access to the besieged city because a section of the eastern shore remained in Soviet hands.

Under Ravalomanana these investments produced substantial economic growth but the benefits were not evenly spread throughout the population, producing tensions over the increasing cost of living and declining living standards among the poor and some segments of the middle class.

Under the older Cronquist system the order contained these four " core Malvales " families plus the Elaeocarpaceae and was placed among the Dilleniidae.

Under these circumstances, Soriano was initially very receptive to an offer from a Milwaukee-based group headed by car salesman Bud Selig.

Under the terms of the agreement, the U. S. is to retain its rights to bases on the island, but these are to be nuclear-free.

Under the most favorable assumptions for increase, the Bureau of the Census projects that the annual rate of household formations will rise from about 883,000 in the last two years of the Fifties to an annual rate of about 1,018,000 in the first five years of the Sixties, and to a slightly higher annual rate of 1,083,000 in the second half of the decade.

Under the same constant gravity assumptions, the potential energy, E < sub > p </ sub >, of a body at height h is given by E < sub > p </ sub >

Under standard assumptions the orbital period () of a body traveling along an elliptic orbit can be computed as:

Under standard assumptions the orbital speed () of a body traveling along elliptic orbit can be computed from the Vis-viva equation as:

Under standard assumptions, specific orbital energy () of elliptic orbit is negative and the orbital energy conservation equation ( the Vis-viva equation ) for this orbit can take the form:

Under certain assumptions – such as the enzyme concentration being much less than the substrate concentration – the rate of product formation is given by

Under broad assumptions, government decisions about the efficient scope and level of activities can be efficiently separated from decisions about the design of taxation systems ( Diamond-Mirlees separation ).

Under certain technical assumptions, it has been shown that a Euclidean QFT can be Wick-rotated into a Wightman QFT.

Under the assumptions of the preceding section,

Under the assumptions of the preceding section, we have

Under the assumptions of the preceding section, let P denote the r < sup > th </ sup > derivative of P < sub > n </ sub >.

Under these assumptions, Say's law implies that there cannot be a general glut, so that a persistent state in which demand is generally less than productive capacity and high unemployment results, cannot exist.

Under these assumptions, it follows that the correlation between parallel test scores is equal to reliability ( see Lord & Novick, 1968, Ch.

Under certain assumptions, the production function can be used to derive a marginal product for each factor, which implies an ideal division of the income generated from output into an income due to each input factor of production.

Under more strict assumptions than those above, e. g., if the responses are assumed to be continuous and the alternative is restricted to a shift in location ( i. e. F < sub > 1 </ sub >( x ) = F < sub > 2 </ sub >( x + δ )), we can interpret a significant MWW test as showing a difference in medians.

Under mild assumptions, the Herdan-Heaps law is asymptotically equivalent to Zipf's law ( Kornai 1999, Baeaza-Yates and Navarro 2000, van Leijenhorst and van der Weide 2003 ).

" Under typical statistical assumptions, the mean or average is the statistic for estimating location that minimizes the expected loss experienced under the Taguchi or squared-error loss function, while the median is the estimator that minimizes expected loss experienced under the absolute-difference loss function.

Under certain assumptions ( uniform material, uniform magnetic field, no skin effect, etc.

Under normal assumptions on the coefficient functions p ( x ), q ( x ), and w ( x ) above, they induce a Hermitian differential operator in some function space defined by boundary conditions.

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

Under certain assumptions and for specific quantitative definitions of risk and return, MPT explains how to find the best possible diversification strategy.

# Under certain statistical assumptions, the regression analysis uses the surplus of information to provide statistical information about the unknown parameters β and predicted values of the dependent variable Y.

Under these assumptions the Tikhonov-regularized solution is the most probable solution given the data and the a priori distribution of, according to Bayes ' theorem.

Under standard assumptions a body traveling along an escape orbit will coast along a parabolic shaped trajectory to infinity, with velocity relative to the central body tending to zero, and therefore will never return.