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.

We wish to maximize total value subject to the constraint that total weight is less than or equal to W. Then for each w ≤ W, define m to be the maximum value that can be attained with total weight less than or equal to w. m then is the solution to the problem.

Then, they were ranked to the east, when they were buried in the 5th and later to the beginning of the 6th c. We can notice a strong Anglo-Saxon influence in the middle of the period, that disappears later.

Then, when We decreed ( Solomon's ) death, nothing showed them his death except a little worm of the earth, which kept ( slowly ) gnawing away at his staff: so when he fell down, the Jinns saw plainly that if they had known the unseen, they would not have tarried in the humiliating Penalty ( of their Task ).

Francis A. Schaeffer, an American theologian based in Switzerland, seizing upon the exclusion of the divine from most humanist writings, argued that rampant secular humanism would lead to moral relativism and ethical bankruptcy in his book How Should We Then Live: The Rise and Decline of Western Thought and Culture ( 1976 ).

Some of these songs, along with others performed but not included on the album, were included on Colin Newman's post-Wire solo albums ( 5 / 10, We Meet Under Tables ), while others were released by Gilbert and Lewis ' primary post-Wire outlet Dome ( And Then ..., Ritual View ).

Then on 11 April, was a riot in Brixton and when on 13 April Thatcher was quoted Powell's remark that " We have seen nothing yet " by an interviewer she replied: " I heard him say that and I thought it was a very very alarming remark.

" We have no slaves at home – Then why abroad?

Examples: William Faulkner in A Rose for Emily ( Faulkner was an avid experimenter in using unusual points of view-see his Spotted Horses, told in third person plural ); Frank B. Gilbreth and Ernestine Gilbreth Carey in Cheaper By the Dozen ; Frederik Pohl in Man Plus ; and more recently, Jeffrey Eugenides in his novel The Virgin Suicides and Joshua Ferris in Then We Came to the End.

Those songs that went the distance on other charts, but not Billboard ( although all were top five hits on the Billboard chart ), are " Here We Are " and " Then Again " ( 1991 ); " Born Country " and " Take a Little Trip " ( 1992 ); " Once Upon a Lifetime " ( 1993 ); " Give Me One More Shot ," " She Ain't Your Ordinary Girl " and " In Pictures " ( 1995 ); " Sad Lookin ' Moon " ( 1997 ); and " How Do You Fall in Love " ( 1998 ).

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 they made it down to half that size, then they made it to half that size ... We are going over to say hello.

Then Chairman of the Federal Reserve Alan Greenspan was a critic of the system, saying, “ We are, in effect, attempting to use government to enforce two different prices for the same itemnamely, government-mandated deposit insurance.

Congresswoman and 2012 United States presidential candidate Michele Bachmann has cited Schaeffer's documentary series How Should We Then Live?

** How Should We Then Live?

Then, after gaining much media attention, he placed ads in the newspapers that announced, " We nail a lie ", and included a photo of Lawrence.

Then the Cardinal Bishop of Porto said: We supplicate you, Almighty God, effect your customary devotion and pour out on this your servant, __, the grace of the Holy Spirit that he who is constituted at the head of our church as the servant of the mystery, you would strengthen with the fullness of virtue.

Other words commonly sung to the same melody include six Christian hymns ( Be Still, My Soul ; I Sought the Lord ; We Rest on Thee ; A Christian Home ; This Is My Song ; and I Then Shall Live ), Gweddi dros Gymru or A Prayer for Wales ( a national song of Wales ), Ambrosian Oaks ( the alma mater of St. Ambrose University in Davenport, Iowa ), and Land of the Rising Sun ( the national anthem of the short-lived African state of Biafra ).

Other words commonly sung to the same melody include many Christian hymns, namely " Be Still, My Soul "; " We Rest on Thee "; " I Sought the Lord "; " A Christian Home "; " This Is My Song "; and " I Then Shall Live "

We Lived a Life and Then Some: The Life, Death, and Life of a Mining Town.

We can use this fact to prove part of a famous result: for any prime p such that p ≡ 1 ( mod 4 ) the number (− 1 ) is a square ( quadratic residue ) mod p. For suppose p = 4k + 1 for some integer k. Then we can take m = 2k above, and we conclude that

We can consider this an exchange ( Margrabe ) option by considering the first asset to be and the second asset to be the riskless bond paying off $ 1 at time T. Then the call option is exercised at time T when the first asset is worth more than K riskless bonds.

Then Frick offered a slightly better wage scale and advised the Superintendent to tell the workers, " We do not care whether a man belongs to a union or not, nor do we wish to interfere.

* " Come Then, Mortal, We Will Seek Her Soul " ( 1982 )

Then Jennie closed her eyes, stretched forth her arms, and said: `` Take my hand, Louise ; ;

Then Pellieux, turning toward an orderly officer, cried: " Take a cab, and go and fetch General de Boisdeffre.

Two songs, " Then You May Take Me To the Fair " and " Fie on Goodness ," were cut a few months into the run ( though they remain on the cast album ).

Guenevere incites three of them ; Sir Dinadan, Sir Sagramore and the burly Sir Lionel, to engage him in jousting matches (" Then You May Take Me to the Fair ").

Take care of our children ... " Then she melted and disappeared.

and 65daysofstatic on the album Volume 1: Then We Take Japan.

" Green " also featured Nicole Scherzinger as a vocalist on six of the songs on the album including " Flight Response ", " The Real ", " Take Me Back Then ", " Phobics of Tragedy ", " Bring Yourself " and " Last One.

" Thereafter he regularly sang leads on tracks including " Then I Kissed Her ," " Cotton Fields ," " TM Song ," " Take a Load off Your Feet ," " Lookin ' at Tomorrow ( A Welfare Song )," " Peggy Sue ," " Lady Lynda ", " Come Go With Me ", " Good Time ," " Honkin ' Down The Highway " and " Crack at Your Love.

Then the guy said, ' Take off your pants ' and I said, ' Wait a minute.

* If Take, Then Take: Tricks, Half-Tricks and Real Phenomena ( 2005 LP, Limited edition of 400 )

... And Then Take You to a Place Where Jars are Kept is the second album and the third release by the Norwegian stoner rock band Thulsa Doom, released in early 2003.

no :… And Then Take You to a Place Where Jars are Kept

Mock The Week ( BBC2 ), Have I Got News For You ( BBC1 ), Michael McIntyre ’ s Comedy Roadshow ( BBC1 ), Never Mind The Buzzcocks ( BBC2 ) Argumental ( Dave UKTV ), The Comedy Store ( Comedy Central ), The Politics Show ( BBC1 ), Sex Bombs ( BBC2 Northern Ireland ), Strictly Dancing: It Takes Two ( BBC2 ), Most Annoying People 2009 ( BBC3 ), Most Annoying People 2008 ( BBC3 ), The ONE Show ( BBC1 ), World Rally: Portugal 2009 ( Dave UKTV ), Saturday Night Live ( ITV1 ), Girls Who Do Comedy ( BBC1 ), The Bigger Picture ( BBC1 ), Mock The Week ( Dave UKTV ), The Blame Game ( BBC N. Ireland ), World ’ s Greatest Stand Up ( Ch4 ), The Stand Up Show ( BBC1 ), The World Stands Up ( Comedy Central ), Comic Side Of 7 Days ( BBC3 ), That ’ s So Last Week ( Ch5 ), Stitch Up ( BBC1 ), Best Of The Comedy Store ( Ch5 ), The Comedy Store-series 2, 4 & 6 ( Ch5 ), So Graham Norton ( Ch4 ), Music Hall Meltdown ( BBC4 ), And Then You Die ( Dave UKTV ), Test The Nation ( BBC1 ), Big Brothers Little Brother ( Ch4 ), Back In The Day ( Ch4 ), Bridget Jones Cultural Icon ( ITV ), 100 Greatest Tearjerkers ( Ch4 ), 100 Greatest Christmas Moments ( Ch4 ), The Comedian ’ s Comedian ( Ch4 ), Who Stole Bob Monkhouse ’ s Jokes ( BBC ), Take The Mike ( ITV ), Life ’ s A Pitch ( BBC1 ), Ladies & Gentlemen ( BBC ), The Loafers ( BBC North ), Notes From The Ditch ( BBC South ), The Jack Docherty Show ( Ch5 ), Don ’ t Drink The Water ( BBC Challenge ), You ’ re Not Yourself Today ( BBC ), Five ’ s Company ( Ch5 ),

Their latest album, First Take Then Shake, was recorded with Detroit House-producer Anthony Shake Shakir.

* First Take Then Shake, 2004, Disko B db123 ( 12 " LP + 7 " single / CD )

*... And Then Take You to a Place Where Jars are Kept ( 2003 )

Then they moved offices of the East German puppet government into East Berlin and began illegally to treat it as the capital of East Germany.

Then Berlin was a free city surrounded by communist-ruled East Germany, represented a " hot spot " of political and ideological controversy for the revolting German students.

Then he moved to the Humboldt University of Berlin ( then called the Friedrich William University ) in 1878 where he continued his study of mathematics under Leopold Kronecker and the renowned Karl Weierstrass.

* Tony le Tissier: Berlin Then and Now, 1992, After the Battle Publishers, ISBN 0-900913-72-X

Then, it was revealed that the original negative had been shipped back to Berlin ( probably due to the efforts of Frank Hensel ) to be stored in the Reichsfilmarchiv vaults.

Then, suddenly, an Allied attack on Berlin began.

Then Walter returned in 1900 to Berlin, where he assumed the post of Royal Prussian Conductor at the Staatsoper Unter den Linden, succeeding Franz Schalk ; his colleagues there included Richard Strauss and Karl Muck.

Then one of all together eight Berlin Wall crossings was opened on the eastern side of the gate, usually not open for East Berliners and East Germans, who from then on needed a hard-to-obtain exit visa.

Then he took a train to Köpenick, east of Berlin, occupied the local city hall with his soldiers and told them to cover all exits.

Then he commandeered two carriages and told the grenadiers to take the arrested men to the Neue Wache in Berlin for interrogation.

Then he moved to Berlin, where he initially was welcomed by the princess Anna Amalia ( the sister of Frederick the Great ), but later fell into disgrace under still opaque circumstances.

Then, a few months later in early 1944, she was shipped to Ravensbrück concentration camp about 50 miles from Berlin.

Then, in 1930, he accompanied Irving Berlin to Hollywood.

Then, in 1889, he attended a course of instruction at the Academy of Mining in Berlin ( in 1916 merged into the Berlin Institute of Technology ).

Then both armies would strike in a northeastern direction towards Potsdam and Berlin.

Then Khrushchev approved the construction of the Berlin Wall in 1961.

Then he went to Friedrich-Wilhelms-Universität in Berlin, Germany for two years ( 1930-31 ) as a fellow of the Rockefeller Foundation.

Then, after a tour as executive officer at NAS Pensacola, he spent two and one-half years — from March 1923 to September 1925 — as an assistant naval attaché, serving at the American embassies at London, Paris, Rome, the Hague, and Berlin.

Then in Berlin, starting in 1970, he became a professor of experimental music and music research, with subsequent visits to the U. S. for other opportunities.

Then he studied German language and literature at Humboldt University in Berlin, where he was an active member of the Catholic Student Community.

Then, he worked for four years as a clinical assistant at the First Medical Clinic of Charité in Berlin.

Then he went to Berlin, where he met Feruccio Busoni.

Then turning to a wider theme Prutz contributed to Onckens university history the two volumes on the political history of Europe during the Middle Ages ( Staatengeschichte des Abendlandes Im Mittelalter, Berlin, 1885-1887 ).