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For and m
: For an example of the simple algorithm " Add m + n " described in all three levels see Algorithm examples.
For example, if the water is 25 ft ( 8 m ) deep, and the anchor roller is 3 ft ( 1 m ) above the water, the scope is the ratio between the amount of cable let out and 28 ft ( 9 m ).
For small values of m like 1, 2, or 3, the Ackermann function grows relatively slowly with respect to n ( at most exponentially ).
For example, with ( m, n )
For the case of a non-commutative base ring R and a right module M < sub > R </ sub > and a left module < sub > R </ sub > N, we can define a bilinear map, where T is an abelian group, such that for any n in N, is a group homomorphism, and for any m in M, is a group homomorphism too, and which also satisfies
For m, n 0 define
For example, taking m to be 1 gives the triangular numbers 0, 1, 3, 6, ....
For instance, " Phnom Penh " will sometimes be shortened to " m ' Penh ".
For example, the cofinality of ω² is ω, because the sequence ω · m ( where m ranges over the natural numbers ) tends to ω² ; but, more generally, any countable limit ordinal has cofinality ω.
For example, the surface tension of distilled water is 72 dyn / cm at 25 ° C ( 77 ° F ); in SI units this is 72 x 10 < sup >− 3 </ sup > N / m or 72 mN / m.
For example, some references, and Wolfram's Mathematica software, define the complete elliptic integral of the first kind in terms of the parameter m, instead of the elliptic modulus k.
For if k, m, and n are integers, and k is a common factor of two integers A and B, then A = nk and B = mk implies A − B = ( n − m ) k, therefore k is also a common factor of the difference.
For example, it is 6-a-side rather than 11, the field is reduced to approximately 40 m x 20 m ; the shooting circles are 9m ; players may not raise the ball outside the circle nor hit it.
For biological molecules the diffusion coefficients normally range from 10 < sup >− 11 </ sup > to 10 < sup >− 10 </ sup > m < sup > 2 </ sup >/ s.
For positive integer m the derivative of gamma function can be calculated as follows ( here γ is the Euler – Mascheroni constant ):
For instance, German-speakers more often described, ( f .) " bridge " with words like ' beautiful ', ' elegant ', ' fragile ', ' peaceful ', ' pretty ', and ' slender ', whereas Spanish-speakers, which use puente ( m .) used terms like ' big ', ' dangerous ', ' long ', ' strong ', ' sturdy ', and ' towering '.
For that purpose, one needs a hash function that maps similar keys to hash values that differ by at most m, where m is a small integer ( say, 1 or 2 ).

For and
* For all S in M, a ( S ) 0.
For example, 7 5 does not imply that 5 7.
For arbitrary n 2 we may generalize this formula, as noted above, by interpreting the third equation for the harmonic mean differently.
For any information rate R < C and coding error ε > 0, for large enough N, there exists a code of length N and rate R and a decoding algorithm, such that the maximal probability of block error is ≤ ε ; that is, it is always possible to transmit with arbitrarily small block error.
Then N < sub > x </ sub > is a directed set, where the direction is given by reverse inclusion, so that S T if and only if S is contained in T. For S in N < sub > x </ sub >, let x < sub > S </ sub > be a point in S. Then ( x < sub > S </ sub >) is a net.
For any luminosity from a given distance L ( r ) N ( r ) proportional to r < sup > a </ sup >, is infinite for a − 1 but finite for a < − 1.
For n 2, the n-spheres are the simply connected n-dimensional manifolds of constant, positive curvature.
For arbitrary square matrices M, N we write M N if M − N 0 ; i. e., M − N is positive semi-definite.
For example, it follows that any closed oriented Riemannian surface can be C < sup > 1 </ sup > isometrically embedded into an arbitrarily small ε-ball in Euclidean 3-space ( there is no such C < sup > 2 </ sup >- embedding since from the formula for the Gauss curvature an extremal point of such an embedding would have curvature ε < sup >- 2 </ sup >).
For example, for any k 1, the following example meets the bounds exactly.
For example: no cube can be written as a sum of two coprime n-th powers, n 3.
For 1 < p, q < ∞ and f ∈ L < sup > p </ sup >( μ ) and g ∈ L < sup > q </ sup >( μ ), Hölder's inequality becomes an equality if and only if | f |< sup > p </ sup > and | g |< sup > q </ sup > are linearly dependent in L < sup > 1 </ sup >( μ ), meaning that there exist real numbers α, β 0, not both of them zero, such that α | f |< sup > p </ sup > = β | g |< sup > q </ sup > μ-almost everywhere.
For α 1 and β 1, the relative error ( the absolute error divided by the median ) in this approximation is less than 4 % and for both α 2 and β 2 it is less than 1 %.
For n 0, let C < sup > n </ sup >( G, M ) be the group of all functions from G < sup > n </ sup > to M. This is an abelian group ; its elements are called the ( inhomogeneous ) n-cochains.
For n 0, define the group of n-cocycles as:
Lemma: For all real numbers x 1, we have x # < 4 < sup > x </ sup >.
For n 1, the homotopy classes form a group.
For the case of k-in-a-row where the board is an n-dimensional hypercube with all edges with length k, Hales and Jewett proved that the game is a draw if k is odd and k 3 ^ n-1 or if k is even and k 2 ^( n + 1 )-2.

For and 4
For example, arrow 17 in Figure 3 portrays the proximal radial epiphysis for boy 34, whereas the same epiphysis for girl 2 is portrayed by arrow 18 in Figure 4.
For an experiment to qualify as a binomial experiment, it must have four properties: ( 1 ) there must be a fixed number of trials, ( 2 ) each trial must result in a `` success '' or a `` failure '' ( a binomial trial ), ( 3 ) all trials must have identical probabilities of success, ( 4 ) the trials must be independent of each other.
For example, the marksman gets 5 shots, but we take his score to be the number of shots before his first bull's-eye, that is, 0, 1, 2, 3, 4 ( or 5, if he gets no bull's-eye ).
For Yokuts, I tabulated these 71 items in five columns, according as they were expressed by 1, 2, 3, 4, and more than 4 stems.
For hundreds of years, the evidence available consisted of ( 1 ) the captain's fragmentary journal, ( 2 ) a highly prejudiced account by one of the survivors, ( 3 ) a note found in a dead man's desk on board, and ( 4 ) several second-hand reports.
For investors whose income is taxed at high rates, though, a tax-free yield of 4 per cent is high.
For the rivers, the 4 represented the Huai, to the ( then ) Southeast ; ;
For example Connecticut applies the following standard to review unpreserved claims: 1. the record is adequate to review the alleged claim of error ; 2. the claim is of constitutional magnitude alleging the violation of a fundamental right ; 3. the alleged constitutional violation clearly exists and clearly deprived the defendant of a fair trial ; 4. if subject to harmless error analysis, the state has failed to demonstrate harmlessness of the alleged constitutional violation beyond a reasonable doubt.
For a 256-bit block, the first row is unchanged and the shifting for the second, third and fourth row is 1 byte, 3 bytes and 4 bytes respectively — this change only applies for the Rijndael cipher when used with a 256-bit block, as AES does not use 256-bit blocks.
For example, the story of the Amazons settling with the Scythians ( Herodotus Histories 4. 110. 1-117. 1 ).
For example, a vertex configuration of ( 4, 6, 8 ) means that a square, hexagon, and octagon meet at a vertex ( with the order taken to be clockwise around the vertex ).
For example, one imperial pint ( 568 ml ) of beer at 4 % ABV contains:
For example, a regular 275ml bottle of WKD contains 1. 4 units, whereas Bacardi Breezer and Smirnoff Ice both contain 1. 5 units of alcohol.
For comparison, Sirius has an absolute magnitude of 1. 4 which is greater than the Sun's absolute visual magnitude of 4. 83 ( it actually serves as a reference point ).
For example, an array of 10 integer variables, with indices 0 through 9, may be stored as 10 words at memory addresses 2000, 2004, 2008, … 2036, so that the element with index i has the address 2000 + 4 × i.
For much of the history of the series ( Volumes 4 through 29 ), settings in Gaul and abroad alternated, with even-numbered volumes set abroad and odd-numbered volumes set in Gaul, mostly in the village.
For comparison, a Roman 1st BC century catapult using stones of 6. 55 kg fired with a kinetic energy of 16, 000 joules, while a mid 19th century 12 pound cannon firing projectiles of 4. 1 kg fired the projectile with a kinetic energy of 240, 000 joules.
For example A ( 4, 2 ) is an integer of 19, 729 decimal digits.
For every 100 females there were 91. 4 males.
For every 100 females age 18 and over, there were 87. 4 males.

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