Then G is called an open subfunctor of F. If F is covered by representable open subfunctors, then, under certain conditions, it can be shown that F is representable.

Then came an even more shocking confession: according to the CIA document, al-Faruq said two senior al-Qaeda officials, Abu Zubaydah and Ibn al-Shaykh al-Libi, had ordered him to ' plan large-scale attacks against U. S. interests in Indonesia, Malaysia, ( the ) Philippines, Singapore, Thailand, Taiwan, Vietnam and Cambodia.

Then, when the U. S. Army Air Forces on the Marianas Islands ran out of conventional thermite incendiary bombs for its B-29 Superfortresses to drop on Japanese cities, its top commanders, such as General Curtis E. LeMay turned to napalm bombs to continue its fire raids on the large Japanese cities.

Then U acts as a copier provided that

Let U be a functor from D to C, and let X be an object of C. Then the following statements are equivalent:

In 1986, a screening of the entire Monkees television series by MTV led to renewed interest in the group, followed by a single (" That Was Then, This Is Now " reached number 20 on the Billboard Hot 100 in the U. S .), a 20th Anniversary Tour, a greatest hits album and a brand new LP, Pool It!

Then, in 1966, the U. S. Congress created a National Council for Marine Resources and Engineering Development.

Twelve Deadly Cyns ... and Then Some, was released worldwide in 1994 ( except in the U. S., where it was held back until the summer of 1995 ).

Then French Prime Minister Dominique de Villepin sent an emergency aid package worth 36 million Euro ($ 57. 6M U. S. dollars ) and deployed approximately five hundred French troops in an effort to eradicate mosquitoes.

Then in 1885, the U. S. Postal Service rejected the use of two words for a post office name, so Rufus submitted just the name Helix and also became the first postmaster in Spring Valley ; the Helix Post Office was operated out of his home.

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, in December 2001, Krispy Kreme opened its first store outside the U. S. in Mississauga, Ontario, Canada, just outside Toronto.

In 1970, these recordings were compiled onto an LP released via their fan club called From Then to You ( U. S. title: The Beatles ' Christmas Album ).

In 2008, U. K. label Stage Door Records released the retrospective collection Shirley Jones — Then & Now featuring twenty-four songs from Jones's musical career, including songs from the films Oklahoma !, Carousel and April Love.

boundary of U. Then

Then whenever F ( X ) would appear in a statement, you can replace it with a new symbol Y of type U and include another statement P ( X, Y ).

Let U be an open set in R < sup > n </ sup > and φ: U → R < sup > n </ sup > an injective differentiable function with continuous partial derivatives, the Jacobian of which is nonzero for every x in U. Then for any real-valued, compactly supported, continuous function f, with support contained in φ ( U ),

Then φ ( U ) is measurable, and for any real-valued function f defined on φ ( U ),

" Then, Fuentes reminded Cárdenas how the U. S. launched a massive manhunt and investigation after the kidnap, torture, and assassination of the DEA agent Enrique Camarena in 1985 in Mexico.

Then it was broadcast, with English-dubbed voices, in the United States and other English-speaking markets, beginning in September, 1966 ( it was first commissioned for U. S. development by NBC Enterprises adapted by Fred Ladd, for syndicated broadcast ).

Then the energy of the vacuum is exactly E < sub > 0 </ sub >.

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 X is reflexive if and only if each X < sub > j </ sub > is reflexive.

Then the cotangent space at x is defined as the dual space of T < sub > x </ sub > M:

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 >.

Then the complex derivative of ƒ at a point z < sub > 0 </ sub > is defined by

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 overall runtime is O ( n < sup > 2 </ sup >).

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, dividing the units of energy ( such as eV ) by a fundamental constant that has units of velocity ( M < sup > 0 </ sup > L < sup > 1 </ sup > T < sup >-1 </ sup >), facilitates the required conversion of using energy units to describe momentum.

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

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.

* David N. Reznick ( 2009 ) The Origin Then and Now: An Interpretive Guide to the Origin of Species ISBN 978-0-691-12978-5.

Let S be a subgroup of G, and let N be a normal subgroup of G. Then:

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 ).

Then the N = 1 alias of is ( and vice versa ).

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 P is the stereographic projection of B with respect to the North Pole N of B.

Then, M ⊗ N is also an A-module, with

Then N < sub > 1 </ sub >( r, f )

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.