Applying the above function to the arguments ( 5, 2 ), we have:

Applying the scheme discussed above on a fairly modern Windows based system typically results in the following drive letter assignments:

Applying these relations to the strings above, one obtains

Applying information diagrams blindly to derive the above definition has been criticised, and indeed it has found rather limited practical application, since it is difficult to visualize or grasp the significance of this quantity for a large number of random variables.

Applying the above bundle map ( pointwise ) to this section yields the pullback of α by φ, which is the 1-form φ < sup >*</ sup > α on M defined by

Applying the above process ( suppose that n

Applying the Nernst Equation above, one may account for these differences by changes in relative K < sup >+</ sup > concentration or differences in temperature.

Applying the formula above we obtain:

Applying the e < nowiki >'</ nowiki > th iterate of F to a ring which contains a field K of p < sup > e </ sup > elements gives us a fixed point set equal to K, similar to the example above.

Applying this value successively to the tones of a chromatic scale, starting from A above middle C with a frequency of 440 Hz, produces the following sequence of pitches:

Applying these formulas to the above equations is trivial in most cases, but the equation for takes more work:

As defined above one can also get degree of freedom using minimum number of coordinates required to specify a position. Applying it:

Applying these figures to the formula we get the equation: Af.

Applying Lagrange's formula with the observation that Ω • r ( t ) = 0 at all times,

Applying the completeness theorem to this result, gives the existence of a model of T where the formula C < sub > T </ sub > is false.

Applying the formula ( AB )< sup > t </ sup >

Applying both sides to e < sub > j </ sub >, the result on each side is the jth partial derivative of f at p. Since p and j were arbitrary, this proves the formula (*).

Applying this estimate to any even power V < sup > k </ sup > of V and using the Künneth formula shows that the eigenvalues of Frobenius on the middle cohomology of a variety V of any dimension d satisfy

Applying the formula at the top shows this to be about 386 cents.

Applying the same formula in Toronto, Jacobs rallied local groups to oppose development of the Spadina Expressway project, while twice being arrested in the process.

Applying the formula, we get:

:- Applying the aforementioned substitution ratios in the formula: ( of hydrogens * factor )/ hydrogens * 1 ) + ( secondary hydrogens * 3. 8 ) + ( tertiary hydrogens * 5 )

Applying the Lagrange interpolation formula to do quadratic interpolation on the inverse of f yields

Applying Ito's formula, we get:

Applying metamaterials to increase performance of antennas has garnered much interest.

Applying the induction rule repeatedly, starting from the independently proved base case, proves many, often infinitely many, other cases.

Applying this technique to the boundary layer equations gives the full turbulent boundary layer equations not often given in literature:

Applying security afterwards often results in an insufficient security model that leaves too many gaps for future attacks.

Applying this rule often adds humor for both players and on-lookers.

Applying patches to firmware poses special challenges: re-embedding typically small code sets on hardware devices often involves the provision of totally new program code, rather than simply of differences from the previous version.

Applying ice, or even cool water, to a tissue injury has an anti-inflammatory effect and is often suggested as an injury treatment and pain management technique for athletes.

The Cholesky decomposition is commonly used in the Monte Carlo method for simulating systems with multiple correlated variables: The correlation matrix is decomposed, to give the lower-triangular L. Applying this to a vector of uncorrelated samples, u, produces a sample vector Lu with the covariance properties of the system being modeled.

Applying gravel to the roads improved their condition markedly, but asphalt and concrete were not used in local roads until around 1930 ( the year West Harrisville Road was paved ).

Applying the same techniques to studying the Hudson Gorge that he had used in the Galápagos, Beebe encountered a surprising variety of sea animals, many of which had previously been thought to be exclusive to the tropics.

Applying to the French classics the rigorous method used with regard to the texts of the Middle Ages, he published the Pensées of Pascal, revised with the original manuscript ( 1887 – 1889 ), and the Provinciales ( 1891 ), edited with notes.

Applying the chaos theory to the second law of thermodynamics, the paradox of irreversibility can be explained in the errors associated with scaling from microstates to macrostates and the degrees of freedom used when making experimental observations.

Applying a flap technique ( first used by Sir Harold Gillies in 1951 ), the spongiform erectile tissue of the penis is removed, and the skin, with its nerves and vascular system ( blood supply ) still attached, is used to create a vestibule area and labia minora, which then are inverted into the neovaginal cavity created in the pelvic tissue.

Applying many of the PLATO concepts used in the late 1970s, E. Clarke Porter led the Drake Training and Technologies testing business ( today Thomson Prometric ) in partnership with Novell, Inc. away from the mainframe model to a LAN-based client server architecture and changed the business model to deploy proctored testing at thousands of independent training organizations on a global scale.

Applying fire to an ecosystem may create habitats for species that have been negatively impacted by fire suppression, or fire may be used as a way of controlling invasive species without resorting to herbicides or pesticides.

Applying himself to this problem, Giacconi worked on the instrumentation for X-ray astronomy ; from rocket-borne detectors in the late 1950s and early 1960s, to Uhuru, the first orbiting X-ray astronomy satellite, in the 1970s.

Applying the democratic principle, we can calculate the influence of these two rotations on the satellite by calculating the relative contributions of these two collections of massenergy to the background gravitational field strength at the satellite's location, and then weighting their contributions on the satellite's " sense of rotation " accordingly.