Then by the Feynman rules, the correction ( from both scalars ) is:

Then England won in 1911 – 12 by four matches to one.

Then Chris Broad scored three hundreds in successive Tests and bowling successes from Graham Dilley and Gladstone Small meant England won the series 2 – 1.

Then by Arzelà – Ascoli theorem the space K is compact.

Then followed Woolwich Common ( 1907 – 1908 ), Pound Park ( 1908 – 1913 ), and Angerstein Lane ( 1913 – 1915 ).

Then he returned to Germany – crowned emperor and apparent victor over the papacy.

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.

Indeed, following, suppose ƒ is a complex function defined in an open set Ω ⊂ C. Then, writing for every z ∈ Ω, one can also regard Ω as an open subset of R < sup > 2 </ sup >, and ƒ as a function of two real variables x and y, which maps Ω ⊂ R < sup > 2 </ sup > to C. We consider the Cauchy – Riemann equations at z = 0 assuming ƒ ( z ) = 0, just for notational simplicity – the proof is identical in general case.

Then the second Cauchy – Riemann equation ( 1b ) asserts that is irrotational:

Then Goursat's theorem asserts that ƒ is analytic in an open complex domain Ω if and only if it satisfies the Cauchy – Riemann equation in the domain.

Then deforestation rates accelerate ( HFHD, high forest cover – high deforestation rate ), and forest cover is reduced ( LFHD.

Then in 1743 he further alienated his father by marrying Antoinette Champion ( 1710 – 1796 ), a devout Roman Catholic.

* 2002 – 2003 California recall: Then Governor of California Gray Davis announces that the state would face a record budget deficit of $ 35 billion, roughly double the figure reported during his reelection campaign one month earlier.

Then, in the time of Pope Gregory VII ( 1073 – 1085 ), canonists who in the Investiture Controversy quoted the prohibition in canon 22 of the Council of Constantinople of 869 – 870 against laymen influencing the appointment of prelates elevated this council to the rank of ecumenical council.

Then, not long before the finish, the Automobile Club de l ' Ouest ( ACO ), organizers of the Le Mans event, informed Ford that the geographical difference in starting positions would be taken into account at a close finish – meaning that the McLaren / Amon vehicle, which had started perhaps behind the Hulme-Miles car, would have covered slightly more ground over the 24 hours and would therefore be the winner.

Then, a major opportunity arose when Fox – buoyed by the returns from The Sound of Music ( 1965 ) – commissioned Kelly to direct Hello, Dolly!

Then, by allying with the rulers of Austria and Prussia, she incorporated the territories of the Polish – Lithuanian Commonwealth, where after a century of Russian rule non-Catholic mainly Orthodox population prevailed during the Partitions of Poland, pushing the Russian frontier westward into Central Europe.

Then in 1968 he became Professor of Informatics at ETH Zürich, taking two one-year sabbaticals at Xerox PARC in California ( 1976 – 1977 and 1984 – 1985 ).

Then – in the only paid employment he ever had – he took a job as a telegraph operator with the Great Northern Telegraph Company working first in Denmark and then in Newcastle-upon-Tyne, and was soon made a chief operator.

Then the formula

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

Then the following formula is an axiom:

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 correct formula for work function is:

Then, by Euler's formula,

Then that formula must be copied into all of the cells in column C, making sure to change the reference to A1 to a new reference for A2, etc.

Then if " Total Sales " view is added to the workbook, the totals would automatically appear there, because the sheet " knows " that is what the formula is for.

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 by the triple-angle formula, and so.

Then X is defined by the formula so X is in ( actually it is in as well since we could bound both quantifiers by n ).

Then the formula is:

Then, using the formula, the asymptotic behavior can be determined as follows:

Then the Black formula states the price for a European call option of maturity T on a futures contract with strike price K and delivery date T ( with ) is

Then we recursively define the truth of a formula in a model:

Then, the van der Pauw formula becomes

Then the final formula in (*) must be true, and φ is also true.

Then the formula

Then, using this Dirichlet series with Perron's formula, one obtains:

Then, Boltzmann's entropy formula gives for the probability distribution function, A = const.

Then the satisfying instances of the resulting 2SAT formula encode solutions to the vertex cover problem, and there is a satisfying assignment with true variables if and only if there is a vertex cover with vertices.

Then, for example, taking the first option gives a formula for IsPrime ( n ) using Wilson's theorem:

Then Adam Pociej, Bishop of Vladimir, in his own name and that of the Ruthenian episcopate, read in Latin the formula of abjuration of the Greek Schism, Bishop Cyryl Terlecki of Lutsk read it in Ruthenian, and they affixed their signatures.

Then we apply the quadratic formula.