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.

Then, after the synthesis engine has mapped the design to a netlist, the netlist is translated to a gate level description where simulation is repeated to confirm the synthesis proceeded without errors.

The algorithm for deciding this is conceptually simple: it constructs ( the description of ) a new program t taking an argument n which ( 1 ) first executes program a on input i ( both a and i being hard-coded into the definition of t ), and ( 2 ) then returns the square of n. If a ( i ) runs forever, then t will never get to step ( 2 ), regardless of n. Then clearly, t is a function for computing squares if and only if step ( 1 ) terminates.

Then the following regression equation is postulated as a description of the process that generated the data:

Life is Real Only Then, When ' I Am ' contains a fragment of an autobiographical description of later years, as well as transcripts of some lectures.

But at sight of Jayadratha and of their beloved wife seated on his car, their fury knew no bounds ). Then follows the exciting description of a battle in which the five pandavas routed the Sauviras, Ikshwakus, Sivis, and Saindhavas and their armies.

" Then Nancy asked Harry what the two men looked like and he gave her a description of them and said she was going to bring it to the police.

Then silence, and there begins a charming hour of description, analysis, anecdote, harmless pun, which clothes the dry bones with poetic imagery, enlivens a hard and fatiguing day with humor, and brightens to the tired listener the details for difficult though interesting study.

In Tex, there is a brief description of Mark, who is original to That Was Then, This Is Now.

Then the FreshDirect Website added a lengthy description of Fedele's role in the uptown Fairway, headlined: HEY FAIRWAY, WHAT ARE YOU AFRAID OF?

Then, they prepare a treatment, a 25-to-30-page description of the story, its mood, and characters.

Then it became clear that this putsch, and more importantly, the role of the Cossacks in these events, would not be understood without a Cossack prehistory, and so I began with the description of the life of the Don Cossacks just before the beginning of World War I.

Another description of this story comes from The Major Classes by ibn Sa'd al-Baghdadi, although this work is based on the former source :" Then occurred the " sariyyah " of Salim Ibn Umayr al-Amri against Abu Afak, the Jew, in month of Shawwal in the beginning of the twentieth month from the hijra, of the Apostle of Allah.

Then follows a geographical description of the country, followed by a model dialogue in the Cornish language.

" Then, comes a description of the literary activity of the Spanish Jews, giving the most important authors and their works.

Then the Englishman concludes this description with an account of the former Emperor's character, by writing, " I shall begin by stating, in plain English, that he is a great liar and a great miser, and from his childhood has been remarkable for his changeable and deceitful temper, and utter disregard of his oath.

Then, instead of collision-based kinetic description for interaction of charged particles in plasma, Vlasov suggests to use a self-consistent collective field created by charged plasma particles.

* Then follows a humorous description of how the subject of the book ( such a schooling or currency ) has developed through the ages.

Then the overall runtime is O ( n < sup > 2 </ sup >).

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 >.

Then the periodic Bernoulli functions P < sub > n </ sub > are defined as

Then, in terms of P < sub > n </ sub >( x ), the remainder

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 ).

For instance, suppose that each input is an integer z in the range 0 to N − 1, and the output must be an integer h in the range 0 to n − 1, where N is much larger than n. Then the hash function could be h

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 a fuzzy subset s: S of a set S is recursively enumerable if a recursive map h: S × N Ü exists such that, for every x in S, the function h ( x, n ) is increasing with respect to n and s ( x ) = lim h ( x, n ).

Then the statistician must analyze the properties of and, which are viewed as random vectors since a randomly different selection of n cases to observe would have resulted in different values for them.

Then for arbitrary ε > 0 there is an embedding ( or immersion ) ƒ < sub > ε </ sub >: M < sup > m </ sup > → R < sup > n </ sup > which is

Let K be a closed subset of a compact set T in R < sup > n </ sup > and let C < sub > K </ sub > be an open cover of K. Then

Then, using a simple greedy algorithm, the easy knapsack can be solved using O ( n ) arithmetic operations, which decrypts the message.

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 t ( n ( c )) =

Then Y = u ( X < sub > 1 </ sub >, X < sub > 2 </ sub >, ..., X < sub > n </ sub >) is a sufficient statistic for θ if and only if, for some function H,