" Then Saoshyant makes the creatures again pure, and the resurrection and future existence occur " ( Zand-i Vohuman Yasht 3: 62 ).

Then, mathematicians started worrying that they were assuming the existence of a continuum of real numbers without proof.

Then in 1913, using this formula as a basis, Albert Einstein and Otto Stern published a paper of great significance in which they suggested for the first time the existence of a residual energy that all oscillators have at absolute zero.

Then Harrington mysteriously disappears, and no one but Forbes remembers his existence.

Then Yājñavalkya described to her the greatness of the Absolute Self, the nature of its existence, the way of attaining infinite knowledge and immortality, etc.

Then Hofmann leaked its existence to the press, after which the church was virtually forced to release the letter to scholars for study, despite previously denying it had it in its possession.

Then a press release surfaced with a photo of the car, putting Volvo in a position where they had to acknowledge its existence.

Then he instructed him in the teaching of advaita — that " Brahman alone is real, and the world is illusory ; I have no separate existence ; I am that Brahman alone.

Then we should be able to require the existence of n such that N − F ( n ) is both positive and a prime number ; and with all the f < sub > i </ sub >( n ) prime numbers.

* Then since 1970 there has been a tie for each decade of the schools existence, the latest being 2010.

Then, after exploring Brazilian mining area BM-C-8, SK Corporation developed an oil field where it confirmed the existence of more than 50 million barrels of oil deposits.

Then they live an inferior existence without any more contact with the sphere.

Then, in early 1988 in " The Neutral Zone ", the last episode of the first season of Star Trek: The Next Generation, Picard explains to a banker from the 20th century that economics are quite different and the pursuit of money is no longer a part of human existence, however earlier in that season in " Encounter at Farpoint ", Beverly Crusher purchased a bolt of fabric, while asking for it to be billed to her account on the USS Enterprise.

Then as the disgrunted group as they were and Raven's return, a disruptive faction began to occur as Raven tried to further injure the groups moraless existence, until Saturn defeated Raven at Fall Brawl: War Games in a match that forced the Flock to disband.

Then they learn of the existence of his Jewish former wife, Judith Auerbach Schiller ( Sophia Loren ), and arrange for her to be smuggled into Palestine via the port of Haifa.

Then there is one eigenvalue λ = 1 with an algebraic multiplicity m of 2.

Then the behavior of the system in the neighborhood of each equilibrium point can be qualitatively determined, ( or even quantitatively determined, in some instances, by finding the eigenvector ( s ) associated with each eigenvalue ).

Then f is a real valued function whose maximum is the Perron – Frobenius eigenvalue.

# A " Min-max " Collatz – Wielandt formula takes a form similar to the one above: for all strictly positive vectors x, let g ( x ) be the maximum value of < sub > i </ sub > / x < sub > i </ sub > taken over i. Then g is a real valued function whose minimum is the Perron – Frobenius eigenvalue.

Then f is a real valued function whose maximum is the Perron – Frobenius eigenvalue.

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 all elements of X equivalent to each other are also elements of the same equivalence class.

Then, in 2007, 12-year-old Badour Shaker died of an overdose of anaesthesia during or after an FGM procedure for which her mother had paid a physician in an illegal clinic the equivalent of $ 9. 00.

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 we could have written a formula of degree k which is equivalent to φ, namely.

It is frequently stated in the following equivalent form: Suppose that is continuous and that u is a real number satisfying or Then for some c ∈ b, f ( c ) = u.

Then the following are equivalent.

Then γ < sub > 1 </ sub > and γ < sub > 2 </ sub > are called equivalent at 0 if the ordinary derivatives of φ ∘ γ < sub > 1 </ sub > and φ ∘ γ < sub > 2 </ sub > at 0 coincide.

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

Then, if opening or cold calling, the player may exchange a large chip for its full equivalent value out of the pot before placing his bet, or if overcalling may place the chip ( announcing that he is calling or raising a lesser amount ) and remove the change from his own bet for the round.

Then the area of the parallelogram with vertices at a, b and c is equivalent to the absolute value of the determinant of a matrix built using a, b and c as rows with the last column padded using ones as follows:

Then the following are equivalent ( see Proposition 4. 3, p. 16, of the reference given below ):

Then the following conditions are equivalent:

Then the following are equivalent:

Then two members of the Cartesian product are equivalent precisely if they are equal almost everywhere on the index set.

Then for each t the measure Q restricted to the unaugmented sigma fields is equivalent to P restricted to

Then the following are equivalent conditions for f to be separable ; that is, to have distinct roots:

) Then F is said to be separable over if the following equivalent conditions are met:

Then A, B and their intersection A ∩ B are homotopy equivalent to circles, so the nontrivial part of the sequence yields

Then and are equivalent: The functor which maps the object of to the vector space and the matrices in to the corresponding linear maps is full, faithful and essentially surjective.

Then the intersection of A and B is an annulus, which is known to be homotopy equivalent to ( and so has the same fundamental group as ) a circle.

Then the following statements are equivalent:

Let S a multiplicatively closed subset of R, i. e. for any s and t ∈ S, the product st is also in S. Then the localization of M with respect to S, denoted S < sup >− 1 </ sup > M, is defined to be the following module: as a set, it consists of equivalence classes of pairs ( m, s ), where m ∈ M and s ∈ S. Two such pairs ( m, s ) and ( n, t ) are considered equivalent if there is a third element u of S such that

Then the following are equivalent.

) Then, for each integer, we define to be the set of all that satisfies the following equivalent conditions.