Then attention can be focused on where interventions might be best applied, and on planning and evaluating those efforts to inform the development of policy and the application of resources.

Then we can solve for f ′.

Then f = u + iv is complex-differentiable at that point if and only if the partial derivatives of u and v satisfy the Cauchy – Riemann equations ( 1a ) and ( 1b ) at that point.

Let R be a domain and f a Euclidean function on R. Then:

Then the probability density function f *( x ) of the size biased population is

Then the image set f ( I ) is also an interval, and either it contains f ( b ), or it contains f ( a ); that is,

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 pair (( A < sub > i </ sub >)< sub > i ∈ I </ sub >, ( f < sub > ij </ sub >)< sub > i ≤ j ∈ I </ sub >) is called an inverse system of groups and morphisms over I, and the morphisms f < sub > ij </ sub > are called the transition morphisms of the system.

* Let the index set I of an inverse system ( X < sub > i </ sub >, f < sub > ij </ sub >) have a greatest element m. Then the natural projection π < sub > m </ sub >: X → X < sub > m </ sub > is an isomorphism.

Let the line of symmetry intersect the parabola at point Q, and denote the focus as point F and its distance from point Q as f. Let the perpendicular to the line of symmetry, through the focus, intersect the parabola at a point T. Then ( 1 ) the distance from F to T is 2f, and ( 2 ) a tangent to the parabola at point T intersects the line of symmetry at a 45 ° angle.

For f a real polynomial in x, and for any a in such an algebra define f ( a ) to be the element of the algebra resulting from the obvious substitution of a into f. Then for any two such polynomials f and g, we have that ( fg ) ( a )

Then ( X × Y, ( π < sub > 1 </ sub >, π < sub > 2 </ sub >)) is a terminal morphism from Δ to the object ( X, Y ) of D × D. This is just a restatement of the above since the pair ( f, g ) represents an ( arbitrary ) morphism from Δ ( Z ) to ( X, Y ).

Then because the construction of f was uniform, this is a recursive function of two variables.

For f ∈ R, define D < sub > f </ sub > to be the set of ideals of R not containing f. Then each D < sub > f </ sub > is an open subset of Spec ( R ), and is a basis for the Zariski topology.

Then the sufficient condition for exact reconstructability from samples at a uniform sampling rate f < sub > s </ sub > ( in samples per unit time ) is:

Then we can translate this system into fuzzy program in such a way that f is the interpretation of a vague predicate Good ( x, y ) in the least fuzzy Herbrand model of this program.

Then f is called an immersion if its derivative is everywhere injective.

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.