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 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 construction, hypothesis testing limits the rate

By construction, h is antipode-preserving, and thus has non-zero degree.

By construction, h extends to the whole upper hemisphere of S < sup > n </ sup >, and as such is null-homotopic.

By 1972, however, with only a minimum of work done on the I-95 right of way and none on the potentially massively disruptive Inner Belt, Governor Francis Sargent put a moratorium on highway construction within the MA-128 corridor, except for a short stretch of Interstate 93.

By 1985, construction was completed and the World Financial Center saw its first tenants.

By the turn of the 21st century, Battery Park City was mostly completed, with the exception of some ongoing construction on West Street.

By the autumn of 1855, the royal apartments were ready, though the tower was still under construction and the servants had to be lodged in the old house.

By the same construction, every locally compact Hausdorff space X is a dense subspace of a compact Hausdorff space having at most one point more than X ..

By 1827, construction on the Dayton-Cincinnati canal began as a way to better transport goods from Dayton to Cincinnati.

By 1973, construction of the Naval Communications Station ( NAVCOMMSTA ) was completed.

By construction, each point on the curve shows productive efficiency in maximizing output for given total inputs.

By 2007, the Falkland Islands had a road network of with a further roads planned for construction link to all occupied mainland settlements by 2013.

By the 16th century the vihuela's construction had more in common with the modern guitar, with its curved one-piece ribs, than with the viols, and more like a larger version of the contemporary four-course guitars.

By June construction had reached the second level platform, and on Bastille Day this was used for a fireworks display, and Eiffel held a celebratory banquet for the press on the first level platform.

By 1953 nearly one-quarter of the government's budget was devoted to road construction.

By 1907, the product had become successful enough to warrant construction of a second factory at Camberwell Green in London.

By 1947, there would be approximately 22, 000 motor courts in operation in the US alone ; a typical 50-room motel in that era cost $ 3000 per room in initial construction costs, compared to $ 12, 000 per room for metropolitan city hotel construction.

By the construction of ~, this definition is independent of the chosen representatives and the corresponding relation is indeed well-defined.

By construction, d * e = 1 mod φ ( n ).

By 1981 overseas construction projects, most of them in the Middle East, accounted for 60 percent of the work undertaken by South Korean construction companies.

By 1989 there were signs of a revival of the overseas construction market — the Dong Ah Construction Company signed a US $ 5. 3 billion contract with Libya for the second phase of Libya's Great Man-Made River Project, which, when all five phases were completed, was projected to cost US $ 27 billion.

By the 8th century, a navigable canal existed between Old Cairo and the Red Sea, but accounts vary as to who ordered its construction — either Trajan or ' Amr ibn al -' As, or Omar the Great.