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We and replace
We can replace the division by a ( possibly faster ) right bit shift: nP ( key ) >> b.
We simply replace by the covariance matrix:
We are allowed to keep the Schrödinger expression for the current, but must replace by probability density by the symmetrically formed expression
We can equally well speak of Diophantine sets of integers and freely replace quantification over natural numbers with quantification over the integers.
Reportedly, when budget estimates reached $ 14 million, the producers attempted to replace Hill with Arthur Hiller ; but abandoned the idea after hundreds of native Polynesians in the cast went on strike, declaring: " We can and will perform only for our friend, Monsieur Hill.
We must replace V by V − b, where b is called the excluded volume.
We can then use the n < sup > th </ sup > backward vector to eliminate the error term and replace it with the desired formula as follows:
Eric Wilson says, " We will never replace the greatness that Sublime did or what Bradley has done.
We can replace the roulette game in the analysis with either the pass line at craps, where the odds of losing are lower, or, or a coin toss game where the odds of losing are 50. 0 %.
Hume, however, stopped short when it came to the positive side of the theory, where God was called upon to replace such connections, complaining that ' We are got into fairy land [...] Our line is too short to fathom such immense abysses.
We can replace the gradient of potential using hydrostatic equilibrium, via
We can assume that a < sub > j </ sub > is homogeneous of degree d − deg i < sub > j </ sub > for every j ( otherwise, we replace a < sub > j </ sub > by its homogeneous component of degree d − deg i < sub > j </ sub >; if we do this for every j, the equation x =
We are allowed to hope that soon the moral sciences will replace superstition with knowledge about ethics.
We have in effect undertaken to dispense with the forces which produced unforeseen results and to replace the impersonal and anonymous mechanism of the market by collective and ‘ conscious ’ direction of all social forces to deliberately chosen goals .” Socialism, while presented as a means of assuring equality, does so through “ restraint and servitude ”, while “ democracy seeks equality in liberty ”.
We replace all instances of j in the tables with i. Then, we fill in all possible entries of the tables, possibly leading to more deductions and coincidences.
In the build up to the 2006 – 07 season, Ferguson was quoted saying that he planned to replace the departing Van Nistelrooy ( signed by Real Madrid ) by returning Smith to his natural position of centre-forward: " We are going to convert Alan Smith back into being a forward.
We aren't trying to replace the original ; that's impossible anyway.
We may then consider the collection where we replace the two sets and
We shall replace the drawing-room setting with the setting of the theatre itself, our intention being solely to provide a background for all imaginable actions.
Flouride used " an Acoustic 150b amp, and an Acoustic 402 cabinet with stock speakers at last thru ' In God We Trust '", before getting a Traynor Mono Block B amp to replace the Acoustic head.
Previous crusades have included: “ How Much Daylight Are We Really Saving ,” a recommendation for a revised Daylight Saving Time schedule ( 2007 ); “ Why is Good Service So Hard to Schedule ,” recommending that service providers offer more specific timeframes when scheduling home visits ( 2006 ); “ A Kinder, Gentler Nation ,” urging readers to exercise more common courtesy ( 2003 ); “ Saturday: The Trick to Making Halloween a Real Treat ,” advocating that the observance of Halloween be moved to the last Saturday in October ( 1999 ); “ A Cure for Doctors ’ Office Delays ,” demanding more prompt medical service and calling for a “ Patients ’ Bill of Rights ” ( 1996 ); and “ Pennies Make No Sense ,” which sought to eliminate the penny, and to permanently replace the dollar bill with less costly-to-produce dollar coins ( 1989 ).
We want to get the word out to as many people as possible because the agenda of the Christian right is to replace the Constitution with biblical law ," said Kathleen Damiani, president of TheocracyWatch.
" Warner then told the Beach Boys to drop what the company perceived as the weakest track, " We Got Love ," and replace it with the Wilson-Parks tune.
" ( short for Volunteers, the nickname / mascot for the University of Tennessee ) Also, when the cheer was played before kickoff, fans would replace the lyrics " We just " with " We're gonna.

We and r
< li > gcd ( a < sup > r / 2 </ sup > ± 1, N ) is a nontrivial factor of N. We are done .</ li >
We are observing this sequence until a predefined number r of failures has occurred.
) We can be more specific in light of the definition above: Plugging in F = 1 dyne, q < sub > 1 </ sub >= q < sub > 2 </ sub >= 1 statC, and r
We can prove the cancellation law easily using Euclid's lemma, which generally states that if an integer b divides a product rs ( where r and s are integers ), and b is relatively prime to r, then b must divide s. Indeed, the equation
We will redo the record, open up the doors for it to get on the r & b charts and make the black stations to play the record ...
We wish to show ( for small enough values of n ) that it is possible to color the edges of the graph in two colors ( say red and blue ) so that there is no complete subgraph on r vertices which is monochromatic ( every edge colored the same color ).
We calculate the expected number of monochromatic subgraphs on r vertices as follows:
We prove that R ( r, s ) exists by finding an explicit bound for it.
We can obtain a formula for r by substituting estimates of the covariances and variances based on a sample into the formula above.
We define the representation Ψ: R → B ( L < sup > 2 </ sup >( R )) by Ψ ( r )
We can embed the rational numbers into the reals by identifying the rational number r with the equivalence class of the sequence ( r, r, r, …).
( We put the " r " in brackets to avoid confusion with an exponent.
We want to choose β and r < nowiki >'</ nowiki > so that the invariants described above hold.
He was referenced by Richie Rich in Tupac Shakur's song " Rather Be Ya Nigga ", in the line, " Smoke blunts, but leave them stunts up to Super Dave ," in the Ice Cube song " Wicked ", with the line " We'll have to break his ass up like Super Dave ," in the A Tribe Called Quest song " The Chase, Part II " with the lyric, " We flippin ' on niggas like we Super Dave ," in the Cool Calm Pete song " Lost " with the line " You ( r ) fake stunts that's strictly for Super Dave ".
We call the resulting graph the Turán graph T ( n, r ).
We define ( r, f ) in the same way as N ( r, f ) but without taking multiplicity into account ( i. e. we only count the number of distinct poles ).
We can define an even finer equivalence relation of oriented C < sup > r </ sup > curves by requiring φ to be φ ‘( t ) > 0.
We also have the exterior derivative which maps Ω < sup > r </ sup >( M )< sup > C </ sup > to Ω < sup > r + 1 </ sup >( M )< sup > C </ sup >.

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