By applying this general principle, a great number of complex compounds of osmium, ruthenium, iridium, and rhenium, with triphenylphosphine, triphenylarsine, and triphenylstibine have been obtained in this laboratory during the past few years.

By 30 July the Greek army was outnumbered by the counter-attacking Bulgarian army, which attempted to encircle the Greeks in a Cannae-type battle, by applying pressure on their flanks.

By applying the chain rule, the last expression becomes:

By twice applying the transformation above from the stationary to the rotating frame, the absolute acceleration of the particle can be written as:

By 1912 and 1913, there are beginning to be many films from many American companies that rely on applying novel decoration to the story, rather than supplying any twists to the drama itself to sustain interest.

By applying voltage to G, one can control I < sub > D </ sub >.

By applying his construction to the sequence of real algebraic numbers, Cantor produces a transcendental number.

By placing the molecules in wells in the gel and applying an electric field, the molecules will move through the matrix at different rates, determined largely by their mass when the charge to mass ratio ( Z ) of all species is uniform, toward the ( negatively charged ) cathode if positively charged or toward the ( positively charged ) anode if negatively charged.

By applying the variational principle to the action

By charging the right amount of water and applying heat, the system can be brought to any point in the gas region of the phase diagram.

By using this arrangement, many common operations can be implemented by uniformly applying the same operation to each pixel independently.

By applying Pontryagin duality, one can see that abelian profinite groups are in duality with locally finite discrete abelian groups.

By darkening areas of texture maps corresponding to corners, joints and recesses, and applying them via self-illumination or diffuse mapping, a radiosity-like effect of patch interaction could be created with a standard scanline renderer ( cf.

By an offshore drilling contractor effectively applying HSE Management in its organization, it can optimize risk to achieve levels of residual risk that are tolerable.

By applying such principles in an obvious way ( using repeated applications of modus ponens ), Holmes is able to infer from his observation that " the sides of Watson's shoes are scored by several parallel cuts " that:

" By this, James meant that truth is a quality, the value of which is confirmed by its effectiveness when applying concepts to practice ( thus, " pragmatic ").

By applying sprezzatura to his speech and everything else he does, the courtier appears to have grazia and impresses his audience, thereby achieving excellence and perfection.

By applying a bias voltage to a " gate " terminal, the channel is " pinched ", so that the electric current is impeded or switched off completely.

By applying his operational calculus to the analysis of this network he discovered ( 1887 ) what has become known as the Heaviside condition.

By repeatedly applying the definition of conditional probability:

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

By applying the inverse Fourier transform, we can write:

By applying Mauss's theory to data such as Mead's, Lévi-Strauss proposed what he called alliance theory.

By its standard practices of applying good scientific methods, mainstream is distinguished from pseudoscience as a demarcation problem and specific types of inquiry are debunked as junk science, cargo cult science and scientific misconduct etc.

By applying conventional cost-estimating techniques, he concluded that it would cost more than a billion US Dollars to develop this distribution by conventional proprietary means.

By this rule, a tile is drawn whenever a merger is declared.

By the Treaty of Ilbersheim, signed 7 November 1704, Bavaria was placed under Austrian military rule, allowing the Habsburgs to utilise its resources for the rest of the conflict.

By the end of his sole rule ( AD 14 ), Augustus had expanded the empire to the line of the Danube river, which was to remain its central / eastern European border for its entire history ( except for the occupation of Dacia 105-275 ).

By repeating the experiment with particles of inorganic matter he was able to rule out that the motion was life-related, although its origin was yet to be explained.

By the early 20th century, Bulgaria, Greece, Montenegro and Serbia had achieved independence from the Ottoman Empire, but large parts of their ethnic populations remained under Ottoman rule.

By 1857, tensions had again escalated between Mormons and other Americans, largely as a result of accusations involving polygamy and the theocratic rule of the Utah territory by Brigham Young.

By the beginning of the Warring States, progress in astronomy and mathematics allowed the creation of calculated calendars ( where intercalary months and days are set by a rule, and not arbitrarily ).

By 1250, nearly all of Iberia was back under Christian rule with the exception of the small Muslim kingdom of Granada.

By Haitian standards, Magloire's rule was firm, but not harsh: he jailed political opponents, including Fignolé, and shut down their presses when their protests grew too strident, but he allowed labor unions to function, although they were not permitted to strike.

By AD 139, the geographer Ptolemy writes that the " Huni " ( Χοῦνοι or Χουνοἰ ) are between the Bastarnae and the Roxolani in the Pontic area under the rule of Suni.

By the late 13th century, the Siamese kings of Sukhothai had brought most of Malaya under their rule.

By the 16th century western Afghanistan again revereted to Persian rule under the Safavid dynasty.

By these means he consolidated a system of absolute monarchical rule in France that endured until the French Revolution.

By the 18th century, it had transformed itself into the Maratha Empire under the rule of the peshwas ( prime ministers ).

By at least the 11th century BC the island was ruled by a kingdom / chiefdom, and the subsequent transition to aristocratic ( or possibly tyrannic ) rule occurred sometime over the next four centuries.

By the 13th century, Kanem's rule expanded.

By the late 18th century, Bornu rule extended only westward, into the land of the Hausa.

By becoming a protectorate Basotholand and its inhabitants were not subjected to Afrikaner rule, which saved them from experiencing Apartheid, and so generally prospered under more benevolent British rule.

By this rule, the average number of days per year will be 365 + 1 / 4 − 1 / 100 + 1 / 400 = 365. 2425, which is 365 days, 5 hours, 49 minutes, and 12 seconds.

By 1857, tensions had again escalated between Mormons and other Americans, largely as a result of accusations involving polygamy and the theocratic rule of the Utah territory by Brigham Young.

By April 1992, as civilian rule returned, 16 major political parties had been recognized ; 12 major political parties were active in 2004.

By April 1992, as civilian rule returned, 15 political parties had gained recognition.

By the time he returned to Afghanistan in the twenty-first century, his rule was characterized by a lengthy span of peace, but with no significant progress.