[permalink] [id link]
Then X is separable if and only if X ′ is separable.
from
Wikipedia
Some Related Sentences
Then and X
) 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 X is compact if and only if X is a complete lattice ( i. e. all subsets have suprema and infima ).
Then the quotient space X /~ can be naturally identified with a torus: take a square piece of paper, bend and glue together the upper and lower edge to form a cylinder, then bend the resulting cylinder so as to glue together its two open ends, resulting in a torus.
Then a presheaf on X is a contravariant functor from O ( X ) to the category of sets, and a sheaf is a presheaf which satisfies the gluing axiom.
Then the joint distribution of X and Y is completely determined by our channel and by our choice of, the marginal distribution of messages we choose to send over the channel.
* Let the index set I of an inverse system ( X < sub > i </ sub >, f < sub > ij </ sub >) have a greatest element m. Then the natural projection π < sub > m </ sub >: X → X < sub > m </ sub > is an isomorphism.
Then the emf, E < sub > X </ sub >, of the same cell containing the solution of unknown pH is measured.
Then the Zariski tangent space at a point p ∈ X is the collection of K-derivations D: O < sub > X, p </ sub >→ K, where K is the ground field and O < sub > X, p </ sub > is the stalk of O < sub > X </ sub > at p.
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 there is a diagonalizable operator D on V and a nilpotent operator N in V such that ( A ) Af, ( b ) Af.
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 ; ;
Then and separable
For example, let P be an irreducible polynomial with integer coefficients and p be a prime number which does not divides the leading coefficient of P. Let Q be the polynomial over the finite field with p elements, which is obtained by reducing modulo p the coefficients of P. Then, if Q is separable ( which is the case for every p but a finite number ) then the degrees of the irreducible factors of Q are the lengths of the cycles of some permutation of the Galois group of P.
Then the following are equivalent conditions for f to be separable ; that is, to have distinct roots:
Then and are linearly separable if there exists n + 1 real numbers, such that every point satisfies and every point satisfies < math >
0.179 seconds.