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 inserting the energetic definitions of the ionization potential and electron affinity into the Mulliken electronegativity, it is possible to show that the Mulliken chemical potential is a finite difference approximation of the electronic energy with respect to the number of electrons., i. e.,

By inserting the energetic definitions of the ionization potential and electron affinity into the Mulliken electronegativity, it is possible to show that the Mulliken chemical potential is a finite difference approximation of the electronic energy with respect to the number of electrons., i. e.,

By contrast, the second electron resides in the deeper second electron shell, and the second ionization energy required for its removal is much larger: + 4562. 4 kJ per mole.

By applying a high reverse bias voltage ( typically 100-200 V in silicon ), APDs show an internal current gain effect ( around 100 ) due to impact ionization ( avalanche effect ).

By considering every possible combination of the location of the atoms ionized by the alpha particle, Mott showed that the joint probability distribution is overwhelmingly dominated by the case where the trail of ionization is close to a classical path.

By focusing on cases and not on theory, those engaged in moral debate increase the possibility of agreement.

By this consideration atomic physics provides the underlying theory in plasma physics and atmospheric physics, even though both deal with very large numbers of atoms.

By 1928, George Gamow had solved the theory of the alpha decay via tunneling.

By the theory of minute constituents of things, and his emphasis on mechanical processes in the formation of order, he paved the way for the atomic theory.

By contrast, substance theory explains the compresence of properties by asserting that the properties are found together because it is the substance that has those properties.

By giving it the title ' knowledge ', conspiracy theory is considered alongside more ' legitimate ' modes of knowing.

By World War II, control theory was an important part of fire-control systems, guidance systems and electronics.

By 1907 Einstein had framed the fundamentals of the theory of gravity, but then struggled for nearly 8 years with a confounding problem of putting the theory into final form.

By the late nineteenth century, however, a handful of experimental anomalies remained that could not be explained by the simple wave theory.

By comparing different embryonic stages of different vertebrate species, he formulated the Recapitulation theory.

For example, periodic acid according to Kekuléan structure theory could be represented by the chain structure I-O-O-O-O-H. By contrast, the modern structure of ( meta ) periodic acid has all four oxygen atoms surrounding the iodine in a tetrahedral geometry.

By proving that there are ( infinitely ) many possible sizes for infinite sets, Cantor established that set theory was not trivial, and it needed to be studied.

By combining Coulomb's theory with Christian Otto Mohr's 2D stress state, the theory became known as Mohr-Coulomb theory.

By this theory, the name of the Geordie lamp attached to the North East pit men themselves.

By conducting the first ever clinical trial, he developed the theory that citrus fruits cured scurvy.

By using this method students gain the big idea they're taught and later are more willing to learn and keep the specifics of the concept or theory taught.

By the early 20th Century, aether theory was in trouble.

: By spectral theory, we can associate a probability measure to the values of A in any state ψ.

By the early twentieth century, it had been superseded by " number theory ".

( By arithmetic he meant, in part, theorising on number, rather than what arithmetic or number theory have come to mean.

By contrast, there is no consensus against its validity outside of biology ; recapitulation theory is still considered plausible and applied by some researchers in fields like Behavioral Development, the study of the origin of language, and others.