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

Applying the variational principle to the base metric g, one gets the Einstein equations

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

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 ROT13 to a piece of text merely requires examining its alphabetic characters and replacing each one by the letter 13 places further along in the alphabet, wrapping back to the beginning if necessary.

Applying a rotation means here rotating one of the two rods 360 degrees.

Applying thick wraps to both of his knees became a pre-game ritual, and by the end of his career, simply swinging a bat caused him to fall to one knee in pain.

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

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

Applying these relations to the strings above, one obtains

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 for a licence: Currently only one type of licence is available to new applicants, the possession-acquisition licence ( PAL ).

Applying the rule of epoché one sets aside one's initial biases and prejudices in order to suspend expectations and assumptions.

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

Applying the rule of horizontalization one treats each item of description as having equal value or significance.

Applying this concept to human society, Kropotkin presented mutual aid as one of the dominant factors of evolution, the other being self assertion, and concluded that In the practice of mutual aid, which we can retrace to the earliest beginnings of evolution, we thus find the positive and undoubted origin of our ethical conceptions ; and we can affirm that in the ethical progress of man, mutual support not mutual struggle – has had the leading part.

Applying Itō's lemma to the process one gets

Applying the Nernst Equation above, one may account for these differences by changes in relative K < sup >+</ sup > concentration or differences in temperature.

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 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.

Applying a result of MacIntyre on the model theory of p-adic integers, one deduces again that ζ < sub > G </ sub >( s ) is a rational function in p < sup >− s </ sup >.

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 rational basis review the U. S. Supreme Court struck down the ordinance as applied to CLC.

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 this concept, Plato recommended that astronomy be studied in terms of geometrical models and proposed that the elements were particles constructed on a geometrical 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.

* D. Young Computational Chemistry: A Practical Guide for Applying Techniques to Real World Problems, John Wiley & Sons ( 2001 ).

Applying video compression algorithms like MPEG1, MPEG2 or MPEG4 allows for fractional BPP values.

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

* 1887 – Herman Hollerith applies for US patent # 395, 791 for the ' Art of Applying Statistics ' – his punched card calculator.

* 1889 – Herman Hollerith is issued US patent # 395, 791 for the ' Art of Applying Statistics ' — his punched card calculator.

Applying ice for 5 minutes to the muscles reportedly has a sensitivity and specificity of 76. 9 % and 98. 3 %, respectively, for the identification of MG.

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

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

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

* Applying Hungarian notation in a narrower way, such as applying only for member variables helps avoiding naming collision.

Applying Gibbs free energy equation for reactions:

Applying for a COL does not commit the utilities to construct the plant, but it is part of the licensing process, say officials of all the utilities.

Applying black patch to Barbara Loden's head for hole in head illusion ( 1957 )

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.

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 these three sorts of derivatives again to each other gives five possible second derivatives, for a scalar field f or a vector field v ; the use of the scalar Laplacian and vector Laplacian gives two more:

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 Case-Based Reasoning: Techniques for Enterprise Systems ".

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