Then Spec ( A < sub > S </ sub >) is homeomorphic to

Then an element e of S is called a left identity if e * a = a for all a in S, and a right identity if a * e = a for all a in S. If e is both a left identity and a right identity, then it is called a two-sided identity, or simply an identity.

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 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.

Then according to the second isomorphism theorem S ∩ T is normal in T and ST / S ≅ T /( S ∩ T ).

Then, it is undecidable to determine whether the language decided by an arbitrary Turing machine lies in S.

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.

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

“ And that Christ being Lord, and God the Son of God, and appearing formerly in power as Man, and Angel, and in the glory of fire as at the bush, so also was manifested at the judgment executed on Sodom, has been demonstrated fully by what has been said .” Then I repeated once more all that I had previously quoted from Exodus, about the vision in the bush, and the naming of Joshua ( Jesus ), and continued: “ And do not suppose, sirs, that I am speaking superfluously when I repeat these words frequently: but it is because I know that some wish to anticipate these remarks, and to say that the power sent from the Father of all which appeared to Moses, or to Abraham, or to Jacob, is called an Angel because He came to men ( for by Him the commands of the Father have been proclaimed to men ); is called Glory, because He appears in a vision sometimes that cannot be borne ; is called a Man, and a human being, because He appears arrayed in such forms as the Father pleases ; and they call Him the Word, because He carries tidings from the Father to men: but maintain that this power is indivisible and inseparable from the Father, just as they say that the light of the sun on earth is indivisible and inseparable from the sun in the heavens ; as when it sinks, the light sinks along with it ; so the Father, when He chooses, say they, causes His power to spring forth, and when He chooses, He makes it return to Himself.

" Then she carries her sleeping child into the other room and tells him to sleep, while she too falls asleep.

Then the problem is to get stamps to " fill the holes "; only a handful of dealers will have a complete stock, and so the want list may take on a life of its own as the collector carries it to stamp shows, mail copies to out-of-town dealers, and so forth, gradually crossing off entries as they are located and purchased.

Then, the vehicle it carries is lowered by a lift from the Albatross ' cargo, just as it finishes its landing procedure and approach.

Then the male takes all the survivors and carries around the developing young in his vocal pouch.

Then, as he carries her in a piggyback fashion, he talks with her.

Then there are a pair of old biddies played by Grace Carney and Sibly Bowan who may be right off the shelf of stock Irish characters, but they put such a combination of good will and malevolence into their parts that they're quite entertaining.

Then the equivalence class of the pair can be identified with the rational number, and this equivalence relation and its equivalence classes can be used to give a formal definition of the set of rational numbers.

Then, in 1915, William Henry Bragg and William Lawrence Bragg, a British father-son pair, shared this Nobel Prize for their discoveries in the reverse problem-determining the structure of crystals using X-rays.

Then the pair (( A < sub > i </ sub >)< sub > i ∈ I </ sub >, ( f < sub > ij </ sub >)< sub > i ≤ j ∈ I </ sub >) is called an inverse system of groups and morphisms over I, and the morphisms f < sub > ij </ sub > are called the transition morphisms of the system.

Then, the electrons to be placed in the molecular orbitals are slotted in one by one, keeping in mind the Pauli exclusion principle and Hund's rule of maximum multiplicity ( only 2 electrons, having opposite spins, per orbital ; place as many unpaired electrons on one energy level as possible before starting to pair them ).

Then the characteristic ( or defining ) property of the ordered pair is:

Then the pair ( x < sub > 1 </ sub >, y < sub > 1 </ sub >) solving Pell's equation and minimizing x satisfies x < sub > 1 </ sub >

Then, the single-sideband complex signal centered at zero is upconverted to a real signal, by another pair of quadrature mixers, to the desired center frequency.

Then ( X × Y, ( π < sub > 1 </ sub >, π < sub > 2 </ sub >)) is a terminal morphism from Δ to the object ( X, Y ) of D × D. This is just a restatement of the above since the pair ( f, g ) represents an ( arbitrary ) morphism from Δ ( Z ) to ( X, Y ).

Then one way of representing the truth condition of " Nixon is alive " is as the ordered pair < Nixon,

Then while standing in front of a full-length mirror, he committed suicide by stabbing himself with a pair of sewing scissors seven times ( supposedly while surrounded by newspaper clippings of his career ), resulting in lurid press coverage.

Then Maelgwn challenged the pair to a horse race.

Then, from 2001 through 2004, Fordland teams won 63 games while losing only 20, winning a pair of Summit Conference championships and a Class 2 district championship in 2003.

Then the dead person's heart was weighed on a pair of scales, against the goddess Ma ' at, who embodied truth and justice.

Then apply the following 4 rules, in order, to each pair of letters in the plaintext:

Then with 3: 45 left in the half, Tampa Bay drove 77 yards, assisted by a pair of catches by Alstott for 28 total yards.

Then the pair is called a direct system over.

A pair of official live albums, All Night Wrong and Then !, were released in 2002 and 2003, respectively, along with a double compilation album, The Best of Allan Holdsworth: Against the Clock, in 2005.

Then, when asked about how the pair of them had managed to get home a day before the rescue ship carrying the survivors was due, their story begins to unravel ; they say they jumped ship and " ship-hiked " their way home.

Then one seeks vectors maximizing the same correlation subject to the constraint that they are to be uncorrelated with the first pair of canonical variables ; this gives the second pair of canonical variables.

Then, he creates " survey codes " for each pair of the rulers, which contain a number which describes degree of the match of each considered property of two rulers.

Then the pair of vectors W =( F, R × F ) is called a wrench.

Then a new pair of basis points is selected, and the process is repeated.

Then we will study the coordinate transformations between this coordinate and the fixed " laboratory " system.

The other class of Dedekind rings which is arguably of equal importance comes from geometry: let C be a nonsingular geometrically integral affine algebraic curve over a field k. Then the coordinate ring k of regular functions on C is a Dedekind domain.

* Let k be the coordinate ring of the variety V. Then the dimension of V is the transcendence degree of the field of fractions of k over k.

Then using the polar radius of the Earth as the radial coordinate ( or meters ), we find that

Then the Walsh – Hadamard code is the function that maps every string into the string satisfying for every ( where denotes the th coordinate of, identifying with in some way ).

Then where and n is the order of the used generator point P. So are the first L bits of the x coordinate of R.

Let's say a particle in this body has coordinate ( x < sub > 1 </ sub >, y < sub > 1 </ sub >, z < sub > 1 </ sub >) along with x-coordinate ( x < sub > 2 </ sub >) and y-coordinate ( y < sub > 2 </ sub >) of second particle. Then using distance formula of distance between two coordinates we have distance d = sqrt ((( x < sub > 1 </ sub >- x < sub > 2 </ sub >)< sup > 2 </ sup >+( y < sub > 1 </ sub >- y < sub > 2 </ sub >)< sup > 2 </ sup >+( z < sub > 1 </ sub >- z < sub > 2 </ sub >)< sup > 2 </ sup >))

Then, every vector field on the manifold can be written down as a linear combination of the four coordinate basis vector fields:

Then there is a local coordinate system consisting of n complex-valued functions z < sup > 1 </ sup >,..., z < sup > n </ sup > such that the coordinate transitions from one patch to another are holomorphic functions of these variables.

Then you perform a coordinate transformation which moves points around in the future of the initial value surface, but which doesn't affect the initial surface or any points at infinity.

Then you can conclude that the generally covariant field equations don't determine the future uniquely, since this new coordinate transformed metric is an equally valid solution.