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

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 the above formula to the 25-meter-diameter antennas often used in radio telescope arrays and satellite ground antennas at a wavelength of 21 cm ( 1. 42 GHz, a common radio astronomy frequency ), yields an approximate maximum gain of 140, 000 times or about 50 dBi ( decibels above the isotropic level ).

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 formula above we obtain:

:- 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 higher pressure of the order of hundreds or thousands of kilobars induces a series of phase transformations, in particular with a tetragonal phase appearing at about 900 kbar.

Applying Chow's analysis to the case of the unexpected hanging ( again with the week shortened to two days for simplicity ), we start with the observation that the judge's announcement seems to affirm three things:

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 rules and customs of prize law, the courts decided whether the Letter of Marque was valid and current, and whether the captured vessel or its cargo in fact belonged to the enemy ( not always easy, when flying false flags was common practice ), and if so the prize and its cargo were " condemned ", to be sold at auction with the proceeds divided among the privateer's owner and crew.

Applying power to one cathode surrounds it with an orange glow discharge.

Applying a pulse with specified width and voltages to the spades made the sheet advance to the next anode, where it stayed until the next advance pulse.

* Greening The Desert: Applying natural farming techniques in Africa, interview with Masanobu Fukuoka ( retrieved 30 November 2010 )

Applying this recursively gives an algorithm with a multiplicative cost of.

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 Itō's lemma with f ( S ) =

Applying Itō's lemma with f ( Y ) = log ( Y ) gives

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 this with, then and

Applying procedural fairness to an entire society therefore seems certain to create recognizable inefficiencies, and therefore be unfair, and ( by the equivalence of justice with fairness ) unjust.

Applying the rule of description, one occupies oneself with describing instead of explaining.

Applying again Bayes ' theorem, and assuming the classification between spam and ham of the emails containing a given word (" replica ") is a random variable with beta distribution, some programs decide to use a corrected probability:

Applying these methods in the workplace, such as Csikszentmihalyi did with Swedish police officers, can improve morale by fostering a sense of greater happiness and accomplishment, and in correlated to increased performance.

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 the rational root theorem thus yields the following possible roots for t:

Applying this to the function defined by f () = log ( a < sub > 1 </ sub >), we obtain that

Applying Seifert's algorithm to this diagram, as expected, does produce a Seifert surface ; in this case, it is a punctured torus of genus g = 1, and the Seifert matrix is

The ancient geometers are not done yet, for if the fifth vertex of the pentagon is marked as E and FE and BF are joined ( with FE = BF = z ), then cyclic quadrilateral EFBA will be formed with diagonals length d ( diameter ) and b. Applying the ' Almagest ' theorem yet again:

Applying Kummer's 24 = 6 × 4 transformations to the hypergeometric function gives the 6

Applying a delta-v at the LEO of only 0. 78 km / s more ( 3. 20-2. 42 ) would give the rocket the escape speed, while at the geostationary orbit a delta-v of 1. 46 km / s is needed for reaching the escape speed of this circular orbit.

Applying the method to hydrogen, they found that the moment of a proton was 2. 785 ± 0. 02 nuclear magnetons, and not 1 as predicted by the current theory, while that of a deuteron was 0. 855 ± 0. 006 nuclear magnetons.

Applying this to a space of dimension 0, which contains exactly one vector ( the zero vector ), the only candidate for a basis is the empty set ( both because 0 elements are required, and because the zero vector cannot be in any basis ).

Applying the techniques developed at Harvard for generating a paradigm from a representative form and its classification, we can add all forms of a word to the dictionary at once.

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 the two sine waves at frequencies ω < sub > 1 </ sub >

Applying the right amount of inputs in the right place and at the right time benefits crops, soils and groundwater, and thus the entire crop cycle.

Applying the principles of comparative negligence, the jury found that McDonald's was 80 % responsible for the incident and Liebeck was 20 % at fault.

* Applying a Doppler ultrasonic scanner, the surgeon identifies the axial pedicle of the tissue-flap ( composed of the supraorbital artery and the supratrochlear artery ), usually at the base, next to the medial brow ; the point usually is between the midline and the supraorbital notch.

* Free Advice On Applying To Graduate School ( PDF )-Written by a professor of psychology at Portland State University.

Applying Equation ( 1 ) and KCL at the OA's non-inverting input v < sub >+</ sub > gives

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 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 most commonly cited definition of systemic risk, that of the Financial Stability Board ( FSB ), to the core activities of insurers and reinsurers, the report concludes that none are systemically relevant for at least one of the following reasons:

Applying the method hierarchically ( according to the data structure at hand ), optionally in both increasing and decreasing direction, yields highly efficient multidimensional range search which is important in both commercial and technical applications, e. g. as a procedure underlying nearest neighbour searches.

Applying to him the term " absolute " would, however, give a false impression: he is not free to issue decrees at whim.

Applying symmetry reduced the computational and memory requirements associated with the problem, allowing the researchers to obtain results on the supercomputers available at the time.

Applying the physics of high pressure jets exiting circular apertures, a doubling of velocity and gas concentration at a fixed point in the whistle mouth would require a quadrupling of either aperture area or absolute pressure.