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 the Phase correlation method to a pair of images produces a third image which contains a single peak.

Applying the method to itself, Descartes challenges his own reasoning and reason itself.

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 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 method, George concluded that many of the problems that beset society, such as poverty, inequality, and economic booms and busts, could be attributed to the private ownership of the necessary resource, land.

)< ref > Pages 171 – 173, Applying the Pūrana method to solve fourth power equations by completing the fourth power of the binomial, ( x + a )< sup > 4 </ sup >.

Applying Newton's method to ( 4 ) and ( 5 ) we get an equation for update:

Applying the same requirements to all students may not be the most effective teaching method.

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

Applying a standardized method, the plaque pH is measured at least in four volunteers during and for 30 minutes after consumption of the product with an indwelling, interproximally-placed, plaque-covered electrode.

Applying a standardized method, the plaque pH is measured at least in four volunteers during and for 30 minutes after consumption of the product with an indwelling, interproximally placed, plaque-covered electrode.

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 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 principle of indirect rule, the British allowed native authorities to administer populations according to their own traditions.

* Applying any form of simple or complex data validation.

Applying his engineering background, Chanute collected all the data that he could find from flight experimentors around the world.

Applying standards to the process can ensure the data is precise and consistent.

Applying the phrase structure rules in a neutral manner, it is possible to generate many proper sentences of English.

Applying this procedure to the structure sheaf, one recovers the Hilbert polynomial of X.

Applying sealants does not require drilling or removing tooth structure.

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

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

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

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

* 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 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.