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 divergence theorem to the product of a scalar function g and a vector field F, the result is

* Applying the divergence theorem to the cross-product of two vector fields, the result is

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 heat to the inner cable for soldering may weaken the steel, and although soft soldering is less strong than silver solder, a lower temperature is required to form the joint, and there is less likelihood of the inner cable being damaged as a result.

Applying Van Kampen's theorem gives the result.

Applying perspective ( pharmacoeconomic ) to analyze cost reduction, it has been shown that savings made by individual hospitals result in actual cost increases to the Provinces.

Applying a result of linear algebra to both orthogonality relations (| C < sub > i </ sub >| is always positive ), we find that the number of conjugacy classes is greater than or equal to the number of inequivalent irreducible representations ; and also at the same time less than or equal to.

Applying this result repeatedly shows that there is a basis for V such that all elements of the Lie algebra are represented by upper triangular matrices.

Applying excessive force to the cube when twisting it may result in broken pieces.

Applying the result of the previous subsection to the displacement, the velocities in the two reference frames are related by the equation

Applying this method instead of Euler's method gives a much better result ( blue ).

Applying finding from affective forecasting research to happiness also raises methodological issues: should happiness measure the outcome of an experience, or the choice that is satisfied as a result of a forecast?

Applying jpeg compression on every frame can reduce the BPP to 8 or even 1 bits / pixel.

Applying Fubini's theorem and integrating on the fiber, one gets

Applying this objective test, the Court has held Miranda does not apply to roadside questioning of a stopped motorist or to questioning of a person briefly detained on the street — a Terry stop.

Applying the inverse-square law between the charges on the electron and nucleus, one can write:

Applying source separation techniques on the measured signals can help remove undesired artifacts from the signal.

Applying carefully selected rules at the social level and encouraging appropriate motives at the personal level is, so it is argued, likely to lead to a better overall outcome even if on some individual occasions it leads to the wrong action when assessed according to act utilitarian standards.

Applying again the matrix operator on both side yields

Applying the transmission line model based on the telegrapher's equations, the general expression for the characteristic impedance of a transmission line is:

Applying the filter to an input in this form is equivalent to a Direct Form I or II realization, depending on the exact order of evaluation.

Applying a conception of such illocutionary acts according to which they are ( roughly ) acts of saying something with the intention of communicating with an audience, he describes indirect speech acts as follows: " In indirect speech acts the speaker communicates to the hearer more than he actually says by way of relying on their mutually shared background information, both linguistic and nonlinguistic, together with the general powers of rationality and inference on the part of the hearer.

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

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 Clausius inequality on this loop,

Applying an operation on a scene graph requires some way of dispatching an operation based on a node's type.

* CLAVIER: Applying case-based reasoning on to composite part fabrication

Applying for a commercial pilot's licence on 2 June 1921 ( in which he gave his name as ' Charles Edward Kingsford-Smith '), he became one of Australia's first airline pilots when he was chosen by Norman Brearley to fly for the newly formed West Australian Airways.

Applying a little bit of ghee on cotton and keeping it on the navel overnight is considered a remedy for dry lips.

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

He also wrote An Essay on Electricity: Explaining the Theory and Practice of that Useful Science, and the Mode of Applying it to Medical Purposes ( London, 1784 ), which ran to four editions in his lifetime.

Applying information extraction on text, is linked to the problem of text simplification in order to create a structured view of the information present in free text.

* Applying for a job in an " essential " civilian occupation and seeking deferment on those grounds-often this required a letter from the potential draftee's employer to be accepted.

Applying only classical physics and the Bohr model of the atom makes both atomic and molecular ionization entirely deterministic ; that is, every problem will always have a definite and computable answer.

Applying this model to the experiences of Mexican Americans forces one to see Mexican American immigrants as positive additions to the " American melting pot ," in which as more additions are made to the pot, the more equal and accepting society will become.

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

Applying a sinusoidal stress to a Maxwell model gives: where is the Maxwell relaxtion time.

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 the business model of the low-cost carrier air lines, these services aim to offer cheaper alternatives to the established operators in the bus, coach and rail markets, by reducing costs, and offering extremely low fares for the earliest bookings, rising nearer the journey time.

Applying a business model learned from her former boss, Tom McNeill, she began hiring young women and training them in the wild routine, which included such antics as chugging alcohol, setting light to it, then breathing fire.