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

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 pixel operations associated with multiple filters can be achieved simultaneously and without a significant increase in processing time.

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 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 Leibniz's Law to the Ship of Theseus problem, S2 is the same as S1 if, and only if, S2 and S1 have all the same properties and relations.

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 his mathematical prowess to the problem, Piet Hein proposed to use the superellipse which became the hallmark of modern Scandinavian architecture.

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 this algorithm to our problem, and using 10-digit floating-point arithmetic, the solution of greater magnitude, as before, is The other solution is then

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 his mind to the problem of heat, he elaborated a first qualitative temperature scale, comprising about twenty reference points ranging from " cold air in winter " to " glowing coals in the kitchen fire ".

Applying methods first suggested by Finlay, yellow fever was eradicated in Cuba and later in Panama, allowing completion of the Panama Canal.

Applying satisficing to research is a way for researchers to adjust to the vast amount of information today.

Applying the functor F to this sequence, and chopping off the first term, we obtain the chain complex

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

Applying this function to our current state we obtain

Applying the formula above we obtain:

Applying appropriate lowpass filter to get rid of the high frequency component on can obtain the value of the equivalent control, which contains more information about the state of the estimated system.

Applying the Klein-Gordon operator on both sides, remembering that the four-moment is on-shell and that is the Green's function of the operator, we obtain:

Applying these substitutions, we obtain the parametric function:

Applying Laplace transformation results in the transformed PID controller equation

Applying these laws results in a set of simultaneous equations that can be solved either algebraically or numerically.

Applying cyanoacrylate to some materials made of cotton or wool ( such as cotton swabs, cotton balls, and certain yarns or fabrics ) results in a powerful, rapid exothermic reaction.

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

Applying to the study of the French Revolution the rules of historical criticism which had produced such rich results in the study of ancient and medieval history, he devoted himself to profound research in the archives, and to the publication of numerous important contributions to the political, administrative and moral history of that period.

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

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 principle of indifference incorrectly can easily lead to nonsensical results, especially in the case of multivariate, continuous variables.

Applying the operator L to each side of this equation results in the completeness relation, which was assumed true.

Applying the XOR gate's output to a low-pass filter results in an analog voltage that is proportional to the phase difference between the two signals.

) 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.

Applying any additive functor to a split sequence results in a split sequence, so in particular R < sup > 1 </ sup > F ( A )

Applying conservation of momentum and energy leads to these results:

Applying the clipping path results in a hard ( aliased ) or soft ( anti-aliased ) edge, depending on the image editor's capabilities

Applying the state-transition function to a state may yield two possible results: either an element of together with the next state of the stream, or the element of the singleton set 1 as a separate " final state " indicating that there are no more values in the stream.

Applying an infinitesimal supersymmetry transformation to a chiral superfield results in yet another chiral superfield whose F-term, in particular, changes by a total derivative.