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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.
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Then and 2
Then Chris Broad scored three hundreds in successive Tests and bowling successes from Graham Dilley and Gladstone Small meant England won the series 2 – 1.
Then, in 396 BC, Agesilaus crossed into Asia with a force of 2, 000 neodamodes ( freed helots ) and 6, 000 allies ( including 30 spartiates ) to liberate Greek cities from Persian dominion.
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 >.
Then Crapsey decided to make the criterion a stanza of five lines of accentual-syllabic verse, in which the lines comprise, in order, 1, 2, 3, 4, and 1 stresses and 2, 4, 6, 8, and 2 syllables.
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 NTPF became the Afloat Prepositioning Force ( AFP ) and eventually Maritime Prepositioning ship Squadron Two ( MPSRON 2 ) consisting of 20 deep-water pre-positioned logistics ships anchored in the lagoon.
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 >.
Let t and s ( t > s ) be the sides of the two inscribed squares in a right triangle with hypotenuse c. Then s < sup > 2 </ sup > equals half the harmonic mean of c < sup > 2 </ sup > and t < sup > 2 </ sup >.
Then and we
Then suddenly we found ourselves in the middle of another fight, an irrational, an indecent, an undeclared and immoral war with our strongest ( and some had thought noblest ) ally.
Then we have surviving at least one instance of a poem prepared for another, in Naturam non Pati Senium, and perhaps also the De Idea Platonica.
Then China promptly went Communist, and Mr. Truman had to fight the interminable Korean war for the democratization of Korea before we learned how far our writ did `` reach in Asia ''.
Then there's always hobbies, collecting stamps, coins, timetables, salt and pepper shakers, elephants, dogs, dolls, shells, or shall we just say collecting anything your heart desires??
Then we drove on, until there was no more road and we traversed dry rice fields, bouncing across their squat earth walls.
Then think of Delaware Bay and the ocean and you see that we have a supply of power for millions of years to come.
Then we have informed a large number of our crew that when they reach the United States, they will be punished but that in the meanwhile, they may run loose and are expected to perform their jobs in good order.
Schweitzer notes that St. Paul apparently believed in the immediacy of the " Second Coming of Jesus ": " Then we which are alive and remain shall be caught up together with them in the clouds, to meet the Lord in the air: and so shall we ever be with the Lord " ( 1 Thessalonians 4. 17 ).
Then we can express the variables as the sum of the ( time averaged ) mean field () that varies in space and a small fluctuating field () that varies in space and time.
Then we are told that P1 is not sped up, so S1 = 1, while P2 is sped up 5 ×, P3 is sped up 20 ×, and P4 is sped up 1. 6 ×.
" Then we who are alive and remain shall be caught up together with them in the clouds to meet the Lord in the air.
Then, before Detroit realizes it, we will have become an excellent car maker, and the customers will think so too.
Then, considering all three colour channels, and assuming that the colour channels are expressed in a γ = 1 colour space ( that is to say, the measured values are proportional to light intensity ), we have:
Let G be a set and let "~" denote an equivalence relation over G. Then we can form a groupoid representing this equivalence relation as follows.
Then and show
Then, advised by the Architect of the Capitol, the Joint Committee for the Library, traditionally responsible for the works of art in the building, ordered the space cleared and painted in fresco, to show `` the Peace after the Civil War '', `` the Spanish-American War '', and `` the Birth of Aviation '', to match as nearly as feasible Brumidi's technique and composition.
Then, once this claim ( expressed in the previous sentence ) is proved, it will suffice to prove " φ is either refutable or satisfiable " only for φ's belonging to the class C. Note also that if φ is provably equivalent to ψ ( i. e., ( φ ≡ ψ ) is provable ), then it is indeed the case that " ψ is either refutable or satisfiable " → " φ is either refutable or satisfiable " ( the soundness theorem is needed to show this ).
Then, five pages later, she quotes the same passage again, but this time in full, straw and all, to show how witches had hallucinations of flight ( Murray 1921, 105-6 ); she does not realise that she has thereby wrecked her previous rationalistic interpretation of the passage.
Then, we can show that if the game starts with n spots, it will end in no more than 3n − 1 moves and no fewer than 2n moves.
Then both step back into the ring, squat facing each other, clap their hands, then spread them wide ( traditionally to show they have no weapons ).
Then followed Talk Radio UK and he joined Capital Gold in February 1994 and presented a talk show interviewing celebrities from all around the world.
Then, in 1938, a show was held at the Mercury Gallery, in direct defiance of the Whitney Museum, which the group regarded as having a provincial, regionalist agenda.
Then, on the show Roger wants to see the script but Tom tells him that there is no script as its spontaneous improvisation.
Then, the burden shifts to the plaintiff, to affirmatively present evidence to show that they have a reasonable probability of prevailing on the action.
Then, a home viewer is called to answer a trivia question about the show, with the opportunity to win a vacation.
— Then turn the winch, and observe when the sun or moon rise and set in the horizon, and the hour-index will show the times thereof for the given day.
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