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If the starting number is rational then this process exactly parallels the Euclidean algorithm.
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If and starting
In addition to acting and occasionally directing, Campbell has become a writer, starting with an autobiography, If Chins Could Kill: Confessions of a B Movie Actor published on August 24, 2002.
If one set is played, the pieces usually go into the opponent's starting corner, and the number of pieces per side is often increased to 15 ( instead of the usual 10 ).
If two sets are played, the pieces can either go into the opponent's starting corners, or one of the players ' two sets can go into an opposite empty corner.
If three sets are played, the pieces usually go into the opponent's starting corners.
If the team scores a touchdown, starting with the 2010 season, it is required to attempt a 2-point conversion.
If the orientation of the tangent relative to some starting position is θ ( s ), then ρ ( s ) is defined by the derivative dθ / ds:
If the starting point is moved, the rats with hippocampal lesions typically fail to locate the platform.
If the palette is only 64 colors ( so color indexes are 6 bits wide ), the symbols can range from 0 to 63, and the symbol width can be taken to be 6 bits, with codes starting at 7 bits.
If one takes the experimentally observed flow around an airfoil as a starting point, then lift can be explained in terms of pressures using Bernoulli's principle and conservation of mass.
If a player's piece lands on a square containing an opponent's piece, the opponent's piece is captured and returns to the starting area.
If the starting function is the Möbius function itself, the list of functions is:
If they were at different speeds ( different frequencies ), the phase difference is undefined and would only reflect different starting positions.
If either the 2nd player chooses to move to the square diagonal to the first player or the first player's 2nd move is not to this square given the choice, then a starting position before flipping moves commence that differs from the standard Othello position arises.
If one learns of a relative's death more than a week following burial, s / he shall sit Shiva starting on the day of notification, if the shloshim period has not elapsed.
If the starting ore is gadolinite, it is digested with hydrochloric or nitric acid which dissolves the rare-earth metals.
If we suppose that each racer starts running at some constant speed ( one very fast and one very slow ), then after some finite time, Achilles will have run 100 metres, bringing him to the tortoise's starting point.
If an ant were to crawl along the length of this strip, it would return to its starting point having traversed the entire length of the strip ( on both sides of the original paper ) without ever crossing an edge.
If continued the line will meet the starting point and will be double the length of the original strip.
If the conjecture is false, it can only be because there is some starting number which gives rise to a sequence which does not contain 1.
If a player rolls three consecutive 6s, he must return to the starting square ( grid " 1 ") and may not move again until rolling another 6.
If the starting number is irrational then the process continues indefinitely.
If this were a test, it would make most sense for Lear to hear out all three daughters before starting to divide the kingdom.
If two solvents can form a positive azeotrope, then distillation of any mixture of those constituents will result in the distillate being closer in composition to the azeotrope than the starting mixture.
If a solution is known moving from peg A to peg C, then, by renaming the pegs, the same solution can be used for every other choice of starting and destination peg.
If and number
If in any one calculation Ptolemy had had to invoke 83 epicycles all at once, while Copernicus never required more than one third this number, then ( in the sense obvious to Margenau ) Ptolemaic astronomy would be simpler than Copernican.
If your state has no provisions for the numbering of pleasure boats, you must apply for a number from the U.S. Coast Guard for any kind of boat with mechanical propulsion rated at more than 10 horsepower before it can be used on Federal waterways.
If a nation wished to get a head start in physical fitness over all other nations, it would start its kindergarten students on a program of gymnastics the day they entered and thus eliminate a large number of the problems that plague American schools.
If no specific organization plan exists limiting the number of scientists at each salary level, the result is a department top-heavy with high-level, high-salaried personnel ''.
If we thus spent our very first day in the midst of a large number of your people honoring a new hero and a great national achievement, our last day, to us at least, was equally impressive and very moving, even though the crowds were absent and there was almost complete silence.
If a wedge-shaped coating of increasing thickness is removed from a substrate by an instrument like the Hesiometer with a knife of constant rake angle, a number of removal mechanisms are often observed which depend upon the thickness of the coating.
If all the operating variables were varied simultaneously, Af operations would be required to do the same job, and as R increases this increases very much more rapidly than the number of operations required by the dynamic program.
If Rock shows up during the number -- or you hear anything -- give me the signal ''.
If one takes the middle number, 5, and multiplies it by 3 ( the base number of the magic square of three ), the result is 15, which is also the constant sum of all the rows, columns, and two main diagonals.
If so, it might be worth while to assign a future jazz show to a different department -- one with enough confidence in the musical material to cut down on the number of performers and give them a little room to display their talents.
* If it is required to use a single number X as an estimate for the value of numbers, then the arithmetic mean does this best, in the sense of minimizing the sum of squares ( x < sub > i </ sub > − X )< sup > 2 </ sup > of the residuals.
If its minimal polynomial has degree, then the algebraic number is said to be of degree.
If K is a number field, its ring of integers is the subring of algebraic integers in K, and is frequently denoted as O < sub > K </ sub >.
* Let Q be a set enclosed between two step regions S and T. A step region is formed from a finite union of adjacent rectangles resting on a common base, i. e. S ⊆ Q ⊆ T. If there is a unique number c such that a ( S ) ≤ c ≤ a ( T ) for all such step regions S and T, then a ( Q )
If a description of s, d ( s ), is of minimal length ( i. e. it uses the fewest number of characters ), it is called a minimal description of s. Thus, the length of d ( s ) ( i. e. the number of characters in the description ) is the Kolmogorov complexity of s, written K ( s ).
If a ) testimonies conflict one another, b ) there are a small number of witnesses, c ) the speaker has no integrity, d ) the speaker is overly hesitant or bold, or e ) the speaker is known to have motives for lying, then the epistemologist has reason to be skeptical of the speaker's claims.
If we take in our hand any volume ; of divinity or school metaphysics, for instance ; let us ask, Does it contain any abstract reasoning concerning quantity or number?
If a is algebraic over K, then K, the set of all polynomials in a with coefficients in K, is not only a ring but a field: an algebraic extension of K which has finite degree over K. In the special case where K = Q is the field of rational numbers, Q is an example of an algebraic number field.
If the two carbon atoms at the double bond are linked to a different number of hydrogen atoms, the halogen is found preferentially at the carbon with fewer hydrogen substituents ( Markovnikov's rule ).
If F is an antiderivative of f, and the function f is defined on some interval, then every other antiderivative G of f differs from F by a constant: there exists a number C such that G ( x ) = F ( x ) + C for all x.
If there is no number to its left, simply look at the column headed " 1 " in the previous row.
If the game has been scored correctly, the total number of plate appearances for a team should equal the total of that team's runs, men left on base, and men put out.
If the other player also knows to offer sacrifices, the expert also has to manipulate the number of available sacrifices through earlier play.
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