Then an arithmetic function a is

Then Fischer and Rabin ( 1974 ) proved that any decision algorithm for Presburger arithmetic has a worst-case runtime of at least, for some constant c > 0.

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

Then angle APB is the arithmetic mean of the angles AOB and COD.

Then the primary arithmetic has the following sentential reading:

Then he said, `` Never noticed it before I mean, when she was dressed but for a woman her age, Julia had a real fine figure ''.

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 in 1702 the French astronomer Philippe de la Hire used a year he labeled at the end of years labeled ante Christum ( BC ), and immediately before years labeled post Christum ( AD ) on the mean motion pages in his Tabulæ Astronomicæ, thus adding the designation 0 to Kepler's Christi.

) 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

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 FG is the harmonic mean of AB and DC.

Then h is half the harmonic mean of A and B.

Then the mean and standard deviation of heights of American adults could be calculated as:

Then the joint distribution of is multivariate normal with mean vector and covariance matrix

Let be the mean of the values in associated with class c, and let be the variance of the values in associated with class c. Then, the probability of some value given a class,, can be computed by plugging into the equation for a Normal distribution parameterized by and.

Then, Phil Sadowski began dredging around the island, adding to its size and increasing its height to six feet above mean sea level, and later built developments on the island.

As Superman brings Lucy back to the window of her apartment, Ricky is furious, and at one point yells, "... In all of the fifteen years we've been married ..." Then Superman says, " You mean to tell me that you've been married to her for fifteen years?

Then, mimicking a technique from The Bob Newhart Show, in which one of the Hartleys flicks back on a bedside light and continues the conversation, Emily turns her bedside lamp on again, slides over and looks down at Bob: " What do you mean, ' beautiful blonde '?!?

Abstractly, we can say that D is a linear transformation from some vector space V to another one, W. We know that D ( c ) = 0 for any constant function c. We can by general theory ( mean value theorem ) identify the subspace C of V, consisting of all constant functions as the whole kernel of D. Then by linear algebra we can establish that D < sup >− 1 </ sup > is a well-defined linear transformation that is bijective on Im D and takes values in V / C.

Then one would find the actual velocity fluctuating about a mean value:

Then, each student ’ s score would be a realization of one of a set of independent and identically distributed random variables, with a mean of 50.

Then, each configuration's change in free energy can be calculated as the potential mean force.

Then FG is the harmonic mean of AB and DC:

Then, the particular face was caricatured simply by subtracting from the particular face the corresponding point on the mean face ( the origin being placed in the middle of the face ), scaling this difference by a factor larger than one, and adding the scaled difference back on to the mean face.

Then all the numbers in the table would be multiplied by one hundred, but it does not mean all the world's currencies just got weaker.

Then the last prime number worth testing as a possible factor of n is P ( i ) where P ( i + 1 )< sup > 2 </ sup > > n ; equality here would mean that P ( i + 1 ) is a factor.

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 ; ;