By strengthening the differentiability assumption, it has been possible to derive second and higher order theories of viscoelasticity.

By convention, the longest serving state governor holds a dormant commission, allowing an assumption of office to commence whenever a vacancy occurs.

By the turn of the century, ethnic self-determination had become an assumption held as being progressive and liberal.

Eudoxus used 27 concentric spherical solids to answer Plato's challenge: " By the assumption of what uniform and orderly motions can the apparent motions of the planets be accounted for?

According to a story reported by Simplicius, Plato posed a question for Greek astronomers: " By the assumption of what uniform and orderly motions can the apparent motions of the planets be accounted for?

By applying a single spatial model on an entire domain, one makes the assumption that is a stationary process.

By expanding the left hand side and then comparing the real and imaginary parts under the assumption that x is real, it is possible to derive useful expressions for cos ( nx ) and sin ( nx ) in terms of cos x and sin x.

By our assumption, the matrix associated to a list of intervals will remain essentially unchanged from one time step to the next.

By late 1981 Pastorius was putting together the Word of Mouth Big Band ( which included Erskine ) for concert dates in Japan, on the assumption that 1982 would be a Weather Report rest year.

By contrast to the notion of civil tolerance, in early modern Europe the subjects were required to attend the state church ; This attitude can be described as territoriality or religious uniformity, and its underlying assumption is brought to a point by a statement of the Anglican theologian Richard Hooker: " There is not any man of the Church of England but the same man is also a member of the commonwealth ; nor any man a member of the commonwealth, which is not also of the Church of England.

By inductive assumption, is the length of some path from source to u.

By inductive assumption, after i − 1 cycles is at most the length of this path.

By the end of 1949, an assumption was made that Rajaji, already Governor-General, would continue as President.

By assuming an indeterministic universe libertarian philosophical constructs can be proposed under the assumption of physicalism.

By far the most common problem in discourse since the Enlightenment is the assumption of the existence of a God's eye view.

By the fundamental assumption of statistical mechanics, the entropy of this microcanonical ensemble is

By this, Foster critiques the assumption in early environmental sociologists that classical sociological thinkers like Marx were supportive of the " Human Exemptionalist Paradigm " and neglectful of environmental conditions in their analysis.

By Newton's third law and the ideal gas assumption, the net force on the system is the force applied by the walls of their container, and this force is given by the pressure P of the gas.

By relying on the result of one cell from the multi-cell embryo, PGD operates under the assumption that this cell is representative of the remainder of the embryo.

By assumption, each entry in the diagonal of P is 1, so the trace of P is n. Applying the inequality of arithmetic and geometric means,

By assumption, c, e, and b + d are integers.

By the assumption that P has width w, and by the finite version of Dilworth's theorem, every finite subset S of P has a w-colorable incomparability graph.

By the end of the Russian Civil War and the introduction of New Economic Policy ( partially supported by Trotsky ) the idea of the labor army ended, especially after Joseph Stalin's assumption of power and the implementation of his policies of industrialization and collectivization, which effectively solved the problem of workforce mobilization both in industry and agriculture.

By the assumption that the energy eigenvalues diverge, the Hamiltonian H is an unbounded operator, therefore we have invoked the Borel functional calculus to exponentiate the Hamiltonian H. Alternatively, in non-rigorous fashion, one can consider that to be the exponential power series.

By June 23, the situation appeared to have normalised, with members of the House of Ariki accepting to return to their regular duties.

By the late 1970s, RCA decided to remove Atkins from his producing duties and replace him with younger men.

By the end of 383 he found his health too feeble to cope with episcopal duties.

By the early 19th century, encouraged by lower duties on gin, the gin houses or " Gin Palaces " had spread from London to most cities and towns in Britain, with most of the new establishments illegal and unlicensed.

By 1944, with the concentration camps fully integrated with the Waffen-SS and under the control of the WVHA, a standard practice developed to rotate SS members in and out of the camps, based on manpower needs and also to give assignments to wounded Waffen-SS officers and soldiers who could no longer serve in front-line combat duties.

By an overall majority, the Senate is the institution that authorizes the Government to adopt measures to enforce an autonomous community's compliance with its constitutional duties when it has failed to do so.

By the action of the Emperor Maximilian and of other German princes they were, in the 16th century, once more restricted to Westphalia, and here, too, they were brought under the jurisdiction of the ordinary courts, and finally confined to mere police duties.

By the start of the 17th century ' jachts ' came in two broad categories-speel-jachts for sport and oorlog-jachts for naval duties.

By 1776, the position of the British Secretary at War was a sophisticated managerial role, but the duties in 1661 to 1666 of England's first Secretary at War, Sir William Clarke, were more basic ones of literally handling the secretarial duties of managing official correspondence, memoranda, military orders, and financial accounts.

By the end of the fifth season, Elliott was gone ( he did appear in the first filmed episode of season six ), and Lupus remained in the last two seasons, with Armitage being given a larger share of screen time and more demanding duties.

By the summer of 1975, those duties became complex enough that Gygax himself became a full-time employee of the partnership in order to take them over from Donna Kaye.

By 1371, the Black Prince was no longer able to perform his duties as Prince of Aquitaine, and returned to England, where plague was wreaking havoc.

By 1980, he was sharing lead singer duties.

By contrast, there are very limited statutory duties imposed on local authorities within an AONB and there is evidence to indicate many residents in such areas may be unaware of the status.

By taking on the duties of serfdom, serfs bound not only themselves but all of their future progeny.

By the end of 1874, Smetana had become completely deaf but, freed from his theatre duties and the related controversies, he began a period of sustained composition that continued for almost the rest of his life.

By mid-August, unable to work, he transferred his duties to his deputy, Adolf Čech.

By December 1790, Hamilton believed import duties, which were the government's primary source of revenue, had been raised as high as was feasible.

By the time of the death of the 6th Baron in 1978, the resultant death duties, coupled with the rising costs of the upkeep, made Belton too much for the Brownlow family.

By 1969, Robinson had voiced his opinion on wanting to retire from the road to focus on raising a family with wife Claudette and their two children, and also focus his duties as Motown's vice president, a job he earned by the mid-1960s after Esther Gordy Edwards had left the position and began mentoring Motown acts on the label's Motortown Revues.

By operation of the CA 343, the State Police was abolished and its military police duties reverted to the PC.

By the 12th century, common law courts in England began using juries for more than administrative duties.

By the late 1990s, remote control locomotives were becoming increasingly popular on North American railroads for use in switching duties in rail yards.

By holding the powers of the tribune, the emperor could prosecute anyone who interfered with the performance of his duties.