Then, using the periodic Bernoulli function P < sub > n </ sub > defined above and repeating the argument on the interval, one can obtain an expression of ƒ ( 1 ).

Ibn Arabi suggested: " The Sufi should shut his door against the world for forty days and occupy himself with remembrance of Allah, that is to keep repeating, " Allah, Allah ..." Then, " Almighty God will spread before him the degrees of the kingdom as a test.

Then by mathematical induction ( infinitely repeating the same step ), one shows there are a yet smaller, then a yet even smaller, example, and hence there must be an infinitude of ever smaller examples.

Then an alternative method of calculating the marginal densities is to create a Markov chain on the space by repeating these two steps:

Then the darkness thinned, and there was light again, and then bright sunlight.

Then they were tumbling again, and the big man reached into the same pocket he had gone for earlier, and came up with a vicious switchblade.

Then Katie stumbled, and again he was falling, falling!!

Then Laura took her gently and shoved her off again, toward Fritzie: Amy did not laugh -- this was work, concentration, achievement.

Then he began to crawl again.

Then she looked at the old woman again, her eyes calm.

Then she fell asleep again as soddenly as a person with fever, and when she awoke it was dark outside and the clarity was back in her eyes.

Then again, there's always that lovely old pastime of hooking or braiding rugs.

Then off again, rushing to keep up.

Then we were off again.

Then I shut off the device again.

`` Then again he might not ''.

Then he attacked the two officers again and was again restrained, Slate related.

Then, after many more billions of years, when all the galaxies are whistling toward a common center, this movement will slow down and reverse itself again.

Then I picked it up again and handed it to the old man.

Then again they would stand in circles making other preparations.

Then they suggested Mu ' awiya ( founder of the Umayyad Caliphate ), but the Caliph again said no.

Then they suggested Abd al-Malik ibn Marwan ( one the greatest of the Umayyad caliphs ), but again no.

Then a " still small voice " comes to Elijah and asks again, " What doest thou here, Elijah?

Then in 794 Kammu suddenly shifted the capital again, this time to Heian-kyō, which is modern day Kyoto.

Then again, who said bad taste was easy?

Then the ban was enforced again by Leo V in 815.

For example, resurrection of the dead, which is exegetically supported by a verse in Exodus 15: " Az Yashir Moshe ..."-" Then will sing ...", from which is derived that " then " ( in the Messianic Era ) Moses will arise and once again sing as he did at the time of the Exodus.

Then the natural dam on the Goulburn River failed, the lake drained, and the Murray River avulsed to the south and started to flow through the smaller Goulburn River channel, creating " The Barmah Choke " and " The Narrows " ( where the river channel is unusually narrow ), before entering into the proper Murray River channel again.

Then they were given 1/2 to 1-1/2 avocados per day as a substitute for part of their dietary fat consumption.

) 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 the pullback of the covector determined by g ( denoted dg ) is given by

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, in the later account found in the Syriac Doctrine of Addai, a painted image of Jesus is mentioned in the story ; and even later, in the account given by Evagrius, the painted image is transformed into an image that miraculously appeared on a towel when Christ pressed the cloth to his wet face.

Then, he wore a Harlequin cap, given to successful cricketers at Oxford.

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 to define multiplication, it suffices by the distributive law to describe the product of any two such terms, which is given by the rule

Then the total number of i-type organisms after the first round of reproduction, given as, is

Then by the law of moment of momentum, the torque on the fluid is given by:

⟨ H ⟩, be the group generated by H. Then the word problem in H < sup >*</ sup > is solvable: given two words h, k in the generators H of H < sup >*</ sup >, write them as words in X and compare them using the solution to the word problem in G. It is easy to think that this demonstrates a uniform solution the word problem for the class K ( say ) of finitely generated groups that can be embedded in G. If this were the case the non-existence of a universal solvable word problem group would follow easily from Boone-Rogers.

Then the solution of the Laplace equation inside the sphere is given by

Then, Pandulf's nephew Pandulf II was given Benevento when Otto II partitioned Landulf IV's territory, with Landulf IV keeping Capua.

Then he ordered 2 golden pieces to be given to every householder in Constantinople and 200 pounds of gold ( including 200 silver pieces annually ) to be given to the Byzantine Church.

Then we imagine the rays are parallel ( and given by two angles ), and we let the colour of a point on the surface be determined by the angle between this direction and the slope of the surface at the point.

Then the formula Cold ( r )→ High ( t ) is true for any t and therefore any t gives a correct control given r. A rigorous logical justification of fuzzy control is given in Hájek's book ( see Chapter 7 ) where fuzzy control is represented as a theory of Hájek's basic logic.

Then the n-th series coefficient c < sub > n </ sub > is given by:

Then, given any point x and neighbourhood G of x, there is a closed neighbourhood E of x that is a subset of G.

Then given the Hamiltonian operator, the equation to satisfy for all functions ( with associated multiplication operator ) is

* Then, to return a new sample given the most recent sample, we proceed as follows:

Then follow the characters of their family and given names.