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Applying and term
Applying the functor F to this sequence, and chopping off the first term, we obtain the chain complex
Applying the Cauchy-Bunyakowski-Schwartz inequality to each term of the last expression yields
Applying to him the term " absolute " would, however, give a false impression: he is not free to issue decrees at whim.

Applying and work
Applying EVM in fast-changing work environments is, in fact, an area of project management research.
Applying the work of Nicolaus Copernicus and other modern scientists, he reveals the principles behind these systems.
Dennis W. Mills discusses the work of Anthony F. Gregorc and Kathleen A. Butler in his article entitled " Applying What We Know: Student Learning Styles ".
Applying these formulas to the above equations is trivial in most cases, but the equation for takes more work:
* Applying learning to their lives and work in the school and community

Applying and Dark
* Allmendinger, Phil and Michael Gunder, 2005, " Applying Lacanian Insight and a Dash of Derridean Deconstruction to Planning's ' Dark Side '," Planning Theory, vol.

Applying and ),
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 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.
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:
* 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 and does
Applying this objective test, the Court has held Miranda does not apply to roadside questioning of a stopped motorist or to questioning of a person briefly detained on the street — a Terry stop.
Applying mineral oil simply darkens the appearance of the stone ; it does not protect it in any way.
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 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 sealants does not require drilling or removing tooth structure.
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
Applying this to both the Earth's and the Moon's position does not disturb the positions relative to each other.

Applying and negative
Applying a negative DC voltage (" bias ") to the control grid will repel some of the electron stream back towards the cathode, thus isolating the plate from the cathode ; full bias will turn the tube off by blocking all current from the cathode.
Applying a negative charge to the photosensitive drum

Applying and word
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 this principle to the art of poetry, and analysing, line by line and even word by word, the works of great poets, he deduced the law that the beauty of poetry consists in the accuracy, beauty and harmony of individual expression.
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:

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