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Page "Cauchy–Riemann equations" ¶ 43
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Then and second
`` Then what about the second interim public announcement??
Then, taking in on the first cable as the boat is motored into the wind and letting slack while drifting back, a second anchor is set approximately a half-scope away from the first on a line perpendicular to the wind.
Then it passed through the oval Forum of Constantine where there was a second Senate-house and a high column with a statue of Constantine himself in the guise of Helios, crowned with a halo of seven rays and looking toward the rising sun.
Then another, even more numerous, army of invaders started a second naval invasion of the Balkans.
Then the first argument becomes conjugate linear, rather than the second.
Then note how the meaning would change if the second premise were parallel to the rest of the syllogism:
Then the second song was played with original members Curt and Cris Kirkwood and new Meat Puppets drummer Ted Marcus.
Then both partners replace weight on the second part of the first beat.
Then repeatedly take the top card from the left hand and transfer it to the right, putting the second card at the top of the new deck, the third at the bottom, the fourth at the top, the fifth at the bottom, etc.
Then according to the second isomorphism theorem S ∩ T is normal in T and ST / S ≅ T /( S ∩ T ).
Then, with the dramatic decrease of oil prices that took place in the second half of 2008 plus the manifest bursting of the real estate bubble, concerns quickly shifted over to the risk of deflation, as Spain recorded in January 2009 its lowest inflation rate in 40 years, followed shortly afterwards, in March 2009 by a negative inflation rate for the first time since the gathering of these statistics started.
Then the composite was rewound and the negative of the second action was copied onto the right side of each frame.
Then on the first play of the Colts ' second drive, Dallas linebacker Chuck Howley intercepted a pass from Johnny Unitas and returned it 22 yards to Baltimore's 46-yard line before being tackled by Unitas himself.
Then on second down and 35 to go, Morton threw a pass that went through the hands of running back Dan Reeves and into the arms of linebacker Mike Curtis, who returned the ball 13 yards to the Cowboys 28-yard line.
Then after throwing an incomplete pass, Terry Bradshaw completed 2 consecutive passes, the second one a 28-yard touchdown completion to Stallworth to take a 7 0 lead.
Then after Dallas ' Dennis Thurman recovered an onside kick at 2: 19, Drew Pearson caught 2 passes for gains of 22 and 25 yards ( the second catch on 4th down and 18 ) as the Cowboys drove 52 yards in 9 plays to score on Staubach's 4-yard touchdown pass to Butch Johnson.
Then on the Bills ' ensuing drive, Kelly was sacked for a 9-yard loss by Stokes, threw an incomplete pass, and then threw his second interception of the game to Edwards, who returned it 35 yards to Buffalo's 33-yard line.
Then, backup quarterback Frank Reich's first pass of the second half was intercepted by Bubba McDowell and returned 58 yards for a touchdown, making the score 35-3.
Then on the second play of the Bills ' next possession, Everett intercepted a pass from Reich and returned it 22 yards to Buffalo's 8-yard line, setting up another touchdown on Smith's 10-yard run.
Then a tunable local oscillator and mixer converts that signal to a second much lower intermediate frequency where the selectivity of the receiver is accomplished.
Then they made an exact, or ' strong ', measurement of the first polarization to see whether it had been disturbed by the second measurement.
Then during the regular-season finale on December 17, 1983, Moseley set an NFL scoring record with 161 points while Riggins ' total of 144 points was second.
Then, Kirchhoff's second rule is used for finding the voltage in the loops ABD and BCD:
Then, in February 1978, before the release of their second single, X-Ray Spex recorded the first of two sessions for John Peel at BBC Radio 1.

Then and Cauchy
Then, since every real is the limit of some Cauchy sequence of rationals, the completeness of the norm extends the linearity to the whole real line.
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 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 the Cauchy product is defined by a discrete convolution as follows.
Then a Cauchy Euler equation of order n has the form
Then there is a neighbourhood of 0 in W on which the quasilinear Cauchy problem
Then, cofinal subsets of A ( or sequences, or nets ) are used to define Cauchy sequences and the completion of the group.
Then the Cauchy problem consists of finding the solution u of the differential equation which satisfies
Then the expressions for the Cauchy stress differences become
Then the true stress ( Cauchy stress ) differences can be calculated as:

Then and
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 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.

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