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:

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!!

Then, Jesus indicated that God's forgiveness is unlimited.

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 it is replaced and fastened.

Then the chines are rounded off and the bottom is rough-sanded in preparation.

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, as the number of users increases, the system becomes even more valuable and is able to attract a wider user base.

Then for each x in I, there is a base element B < sub > 3 </ sub > containing x and contained in I.

Then, for example, (−∞, 1 ) and ( 0, ∞) would be in the topology generated by S, being unions of a single base element, and so their intersection ( 0, 1 ) would be as well.

Then if we intersect each element of B with Y, the resulting collection of sets is a base for the subspace Y.

Then he goes in quest of a sword found in the underworld, at the base of the world-tree, and struggles to bring it back to Asgard.

Then n is palindromic if and only if a < sub > i </ sub > = a < sub > k − i </ sub > for all i. Zero is written 0 in any base and is also palindromic by definition.

Then, on July 1, 1993, the 509th accepted the host responsibilities for Whiteman from the 351st and a new era dawned for the base.

Then the unrestricted wreath product A Wr < sub > Ω </ sub > H of A by H is the semidirect product K ⋊ H. The subgroup K of A Wr < sub > Ω </ sub > H is called the base of the wreath product.

Then the ring is pushed by hand onto the base of the erect penis before releasing the vacuum.

Then as Russian naval activity declined, so did the base and by the early 1900s only a single Russian watchman was left guarding it.

Then in descending order of trim levels were the Caliente, 404 and 202, replacing the previous Custom and base models.

Then governor of the Louisiana Territory, he was on his way to Washington, DC from his base in St. Louis, Missouri.

Then, like many cinder cones, it was snuffed out when several basalt lava flows erupted from its base.

Then the entire Household Division assembly conducts a march past the Queen, who receives a salute from the saluting base.

Then he went to the main Italian military base in Padua, where he agreed with General Armando Diaz on the dissolution of the Italian military mission in Czechoslovakia.

Then, once a strong base is built, the Democrats can work on unifying America.

Then, following Chuichi Nagumo's Indian Ocean raid and raid on Ceylon in early 1942, the Fleet moved its operational base to Kilindini near Mombasa in Kenya, as their more forward fleet anchorages could not be adequately protected from Japanese attack.

Then the closed subscheme determined by the base change is the closed image of X ′.< ref > EGA IV < sub > 2 </ sub >, Proposition 2. 3. 2 .</ ref >

Let be faithfully flat and quasi-compact, and let X ′, Y ′, and f ′ denote the base changes by g. Then for each of the following properties P, f has P if and only if f ′ has P .< ref > EGA IV < sub > 2 </ sub >, Proposition 2. 6. 2, Corollaire 2. 6. 4, and Proposition 2. 7. 1 .</ ref >

This rule base would be searched and the third and fourth rules would be selected, because their consequents ( Then Fritz is green, Then Fritz is yellow ) match the goal ( to determine Fritz's color ).

The rule base is again searched and this time the first two rules are selected, because their consequents ( Then X is a frog, Then X is a canary ) match the new goals that were just added to the list.