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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.
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Then and N
Then there is a diagonalizable operator D on V and a nilpotent operator N in V such that ( A ) Af, ( b ) Af.
Then every linear operator T in V can be written as the sum of a diagonalizable operator D and a nilpotent operator N which commute.
For instance, suppose that each input is an integer z in the range 0 to N − 1, and the output must be an integer h in the range 0 to n − 1, where N is much larger than n. Then the hash function could be h
* David N. Reznick ( 2009 ) The Origin Then and Now: An Interpretive Guide to the Origin of Species ISBN 978-0-691-12978-5.
Then a fuzzy subset s: S of a set S is recursively enumerable if a recursive map h: S × N Ü exists such that, for every x in S, the function h ( x, n ) is increasing with respect to n and s ( x ) = lim h ( x, n ).
Pick a fixed subset L of U. Then the maps F and G, where F ( M ) is the intersection of L and M, and G ( N ) is the union of N and ( U
Then NA < sup > 2 </ sup >+ NB < sup > 2 </ sup >+ NC < sup > 2 </ sup >+ NH < sup > 2 </ sup > = 3R < sup > 2 </ sup > where R is the common circumradius and if PA < sup > 2 </ sup >+ PB < sup > 2 </ sup >+ PC < sup > 2 </ sup >+ PH < sup > 2 </ sup > = K < sup > 2 </ sup >, where K is kept constant, then the locus of P is a circle centered at N with a radius.
Less frequently used is U. N. Owen as for example used in the Agatha Christie novel And Then There Were None.
Then divide the sequence into an initial segment, and a tail of small terms: given any ε > 0 we can take M large enough to make the initial segment of terms up to c < sub > N </ sub > average to at most ε / 2, while each term in the tail is bounded by ε / 2 so that the average is also.
Krayzie Bone also featured on Daz Dillinger's 2008 solo album Only on the Left Side on the song " Meal Ticket " and later on the song " Money Fold ' N " on Tha Dogg Pound's 2009 album That Was Then, This Is Now.
Then, a number X is in the set K ( N ) ( defined above ) if and only if X = d Inv ( d, ( N-1 )/ d ) for some unitary divisor d of N-1.
Then TA is defined to be the subtangent at P. Similarly, if normal to the curve at P intersects the x-axis at N then AN is called the subnormal.
Then χ ( M, N ), defined as the alternating sum of the lengths of the modules Tor < sub > i </ sub >< sup > R </ sup >( M, N ) is 0 if dim M + dim N < d, and positive if the sum is equal to d. ( N. B.
Then and <
Then, p < sup > 2 </ sup > is the fraction of the population homozygous for the first allele, 2pq is the fraction of heterozygotes, and q < sup > 2 </ sup > is the fraction homozygous for the alternative allele.
) Then X < sub > i </ sub > is the value ( or realization ) produced by a given run of the process at time i. Suppose that the process is further known to have defined values for mean μ < sub > i </ sub > and variance σ < sub > i </ sub >< sup > 2 </ sup > for all times i. Then the definition of the autocorrelation between times s and t is
Then I < sub > x </ sub > and I < sub > x </ sub >< sup > 2 </ sup > are real vector spaces and the cotangent space is defined as the quotient space T < sub > x </ sub >< sup >*</ sup > M = I < sub > x </ sub > / I < sub > x </ sub >< sup > 2 </ sup >.
Indeed, following, suppose ƒ is a complex function defined in an open set Ω ⊂ C. Then, writing for every z ∈ Ω, one can also regard Ω as an open subset of R < sup > 2 </ sup >, and ƒ as a function of two real variables x and y, which maps Ω ⊂ R < sup > 2 </ sup > to C. We consider the Cauchy – Riemann equations at z = 0 assuming ƒ ( z ) = 0, just for notational simplicity – the proof is identical in general case.
Then, for any given sequence of integers a < sub > 1 </ sub >, a < sub > 2 </ sub >, …, a < sub > k </ sub >, there exists an integer x solving the following system of simultaneous congruences.
Then the Cartesian product set D < sub > 1 </ sub > D < sub > 2 </ sub > can be made into a directed set by defining ( n < sub > 1 </ sub >, n < sub > 2 </ sub >) ≤ ( m < sub > 1 </ sub >, m < sub > 2 </ sub >) if and only if n < sub > 1 </ sub > ≤ m < sub > 1 </ sub > and n < sub > 2 </ sub > ≤ m < sub > 2 </ sub >.
Then and x
Then G is a group under composition, meaning that ∀ x ∈ A ∀ g ∈ G ( = ), because G satisfies the following four conditions:
Then, Gödel defined essences: if x is an object in some world, then the property P is said to be an essence of x if P ( x ) is true in that world and if P entails all other properties that x has in that world.
Then and is
Then he would get to his feet, as though rising in honor of his own remarkable powers, and say almost invariably, `` Gentlemen, this is an amazing story!!
Certainly, the meaning is clearer to one who is not familiar with Biblical teachings, in the New English Bible which reads: `` Then Jesus arrived at Jordan from Galilee, and he came to John to be baptized by him.
Then it added: `` It is not possible to determine how extensive these ill effects will be -- nor how many people will be affected ''.
Then the words fell into a pattern: `` Mollie the Mutton is scratching her nose, Scratching her nose in the rain.
Then he thought of Aaron Blaustein standing in his rich house saying: `` God is tired of taking the blame.
Then it is marked on the inside where it comes in contact with the transom, frames, keelson and all the battens.
Then, a group of eggs is deposited in a cavity in the beebread loaf and the egg compartment is closed.
Then in 2 we show that any line involution with the properties that ( A ) It has no complex of invariant lines, and ( B ) Its singular lines form a complex consisting exclusively of the lines which meet a twisted curve, is necessarily of the type discussed in 1.
Then, too, the utmost clinical flexibility is necessary in judiciously combining carefully timed family-oriented home visits, single and group office interviews, and appropriate telephone follow-up calls, if the worker is to be genuinely accessible and if the predicted unhealthy outcome is to be actually averted in accordance with the principles of preventive intervention.
Then the editorial added prophetically: `` how far they may reach in Asia is yet undetermined, but they fall far short of our dreams of the war conferences ''.
Then she catapults into `` everything and everybody '', putting particular violence on `` everybody '', indicating to the linguist that this is a spot to flag -- that is, it is not congruent to the patient's general style of speech up to this point.
Then comes the time when the last wire is removed and Susie walks out a healthier and more attractive girl than when she first went to the orthodontist.
Then, with the new affluence, there is actually a sallying forth into the wide, wide world beyond the precincts of New York.
Then, if the middle number is activated to its greatest potential in terms of this square, through multiplying it by the highest number, 9 ( which is the square of the base number ), the result is 45 ; ;
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