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

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

Applying the more detailed form of those calculations to the Ivy Mike device yields vaporized pusher gas expansion velocity of 290 kilometers per second and an implosion velocity of perhaps 400 kilometers per second if 3 / 4 of the total tamper / pusher mass is ablated off, the most energy efficient proportion.

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 definition of the derivative gives:

Applying the definition of functional derivative,

Applying the definition of the reduction semantics, we get the reduction

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 directly the definition of step response

Applying a cost-of-living escalation COLA clause to a stream of periodic payments protects the real value of those payments and effectively transfers the risk of inflation from the payee to the payor, who must pay more each year to reflect the increases in prices.

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

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 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 term to the work of Philip Pullman ( His Dark Materials ), Schweizer clarifies that he does not mean the term to carry the negative connotations of misanthropy: " To me, the word connotes a heroic stance of humanistic affirmation and the courage to defy the powers that rule the universe.

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 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 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 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.

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 this to the geometric progression 31, 62, 124, 248, 496 ( which results from 1, 2, 4, 8, 16 by multiplying all terms by 31 ), we see that 62 minus 31 is to 31 as 496 minus 31 is to the sum of 31, 62, 124, 248.

* Rustum R., A. J. Adeloye, and M. Scholz ( 2008 ) Applying Kohonen Self-organizing Map as a Software Sensor to Predict the Biochemical Oxygen Demand, Water Environment Research, 80 ( 1 ), 32 – 40.

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 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.

* Moores, T. T. & Gregory, Frank Hutson ( 2000 ), " Cultural Problems in Applying SSM for IS Development ", Journal of Global Information Management, vol.

* The Dutch band " Janse Bagge Bend " covered the song in a Dutch dialect in 1983, naming it " Sollicitere ", meaning " Applying " ( for employment ), and featuring it on their album " Flazjelettentaere ".

Applying the same techniques ( which involved gradual immunization of horses and sheep by administering small doses of venoms, and then extracting, purifying and freeze-drying the antibody portion from the blood of injected animals ), Vital Brazil and his coworkers were able to discover the first sera against two species of scorpions ' ( 1908 ) and spiders ' ( 1925 ) venoms.

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 the laws of the psychology of the individual to the nation and to mankind ( for these he considered as social beings ), Lazarus established a new branch of research which he termed " Völkerpsychologie " ( national psychology ).

Applying this subjective case-by-case approach ( known as selective incorporation ), the Court upheld Palko's conviction on the basis that the Double Jeopardy appeal was not " essential to a fundamental scheme of ordered liberty.

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 Jewish Values to Help Heal our Imperiled Planet, ( with Rabbi Yonassan Gershom ), Lulu Press, Inc., Raleigh, North Carolina, 2011 ( ISBN 978-1-105-33646-1 )

* Applying or referring to legal procedures not for the sake of obtaining justice ( or so that justice is served ), but mainly with the aim of making money out of it, or promote one ’ s own position, or to place competitors at a disadvantage.

Applying multiple models that are not integrated within and across an organization could be costly in training, appraisals, and improvement activities.

Applying this rule of thumb, one can apply " common sense " when creating the duration of a single activity or group of activities necessary to produce a deliverable defined by the WBS.

Applying the Tannakian formalism, one concludes that M < sub > num </ sub > is equivalent to the category of representations of an algebraic group G, which is called motivic Galois group.

Applying this age to the base of the Ediacaran assumes that individual cap carbonates are synchronous around the world and that the correct cap carbonate layers have been correlated between Australian and Namibia.

Applying the first three of the five focusing steps of TOC, the system constraint for all projects is identified as are the resources.

Applying Hubble's law to these redshifts, it can be shown that they are between 600 million and 28 billion light-years away ( in terms of proper distance ).

Applying ionophores like valinomycin can create electrochemic gradients that are comparable to the gradients inside the living cell.

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 superposition principle to a quantum mechanical particle, the configurations of the particle are all positions, so the superpositions make a complex wave in space.

Applying a few volts of electricity across silver electrodes drastically enhances the rate bacteria in solution are killed.

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 patches, implementing the principle of least privilege, reducing the attack surface and installing antivirus software are some standard security best practices that are effective against all classes of malware.

Applying the results of local studies to the global scale are complicated by the role the ocean's circulation plays in different ocean regions.

Applying the theory of the Newton polygon for the p-adic number field, for an Eisenstein polynomial, we are supposed to take the lower convex envelope of the points

Applying a few volts of electricity across silver electrodes drastically enhances the rate that bacteria in solution are killed.

Applying this philosophy, we see that social customs are not fixed laws but evolving conventions that serve a purpose in a particular culture and time.

Applying the Theil index to allocation processes in the real world does not imply that these processes are stochastic: the Theil yields the distance between an ordered resource distribution in an observed system to the final stage of stochastic resource distribution in a closed system.

Applying deconvolution successfully to general-purpose camera images is usually not feasible, because the geometries of the scene are not set.

Applying these ladder operators to the eigenstates of the total angular momentum, azimuthal angular momentum and energy operators, the eigenvalues of the first Casimir operator C < sub > 1 </ sub > are n < sup > 2 </ sup > − 1 ; importantly, they are independent of the l and m quantum numbers, making the energy levels degenerate.

Applying the rigid rotor approximation, the energies and degeneracies of the rotational states are given by

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 one of these two processes, short-term redundancy ( positive correlation of nearby values ) of the signal is eliminated ; compression ratios on the order of 2 to 4 can be achieved if differences are subsequently entropy coded, because the entropy of the difference signal is much smaller than that of the original discrete signal treated as independent samples.