Eksempler på brug af Padé på Dansk og deres oversættelser til Engelsk
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Bidraget fra Padé indeholder to forseglede dækker.
Det ville være rimeligt at sige, at dette arbejde er den første systematiske undersøgelse af Padé approximants.
It would be fair to say that this work is the first systematic study of Padé approximants.Padé går videre, og arrangerer approximants, udtrykt hver på sit laveste tal, i en tabel.
Padé goes further, and arranges the approximants, expressed each in its lowest terms, into a table.Også dette var en stor forskel for Padé der blev den yngste leder i Frankrig, da han blev udnævnt.
This too was a high distinction for Padé who became the youngest Rector in France when he was appointed.Henri Padé blev født i Abbeville, som er en by nordvest for Amiens i Picardie-regionen i det nordlige Frankrig.
Henri Padé was born in Abbeville which is a town northwest of Amiens in the Picardy region of northern France.Mellem disse to bidrag fra Frobenius,Darboux havde kigget på Padé approximants af den eksponentielle funktion.
Between these two contributions by Frobenius,Darboux had looked at Padé approximants of the exponential function.De approximants som Padé indført i dette papir er nu kendt som Padé-Hermite approximants.
The approximants which Padé introduced in this paper are now known as the Padé-Hermite approximants.Han viste resultater på deres generelle struktur ogogså klart redegjort for forbindelsen mellem Padé approximants og fortsatte fraktioner.
He proved results on their general structure andalso clearly set out the connection between Padé approximants and continued fractions.Arbejdet i Padé består af en præsentation af hans tidligere resultater vedrørende Padé bordet.
The work of Padé consists of a presentation of his previous results concerning the Padé table.Emile Picard læse to af de redegørelser,herunder den ene af Padé, mens disse andre dommere læse en hver af de resterende tre poster.
Emile Picard read two of the submissions,including the one by Padé, while these other referees read one each of the remaining three entries.Ved 1908 Padé havde skrevet 41 papirer, hvoraf 29 var på fortsatte fraktioner og Padé approximants.
By 1908 Padé had written 41 papers, 29 of which were on continued fractions and Padé approximants.Efter at have afsluttet sine studier på Lycée St Louis, Padé sad indgangen behandling af École Normale supérieure i Paris, ind i École i 1883.
After completing his studies at Lycée St Louis, Padé sat the entrance examination for the École Normale Supérieure in Paris, entering the École in 1883.Padé forsvarede sin afhandling om den 21 juni 1892, eksaminatorer bliver hans vejleder Hermite, sammen med Emile Picard og Paul Appell.
Padé defended his thesis on 21 June 1892, the examiners being his supervisor Hermite, together with Emile Picard and Paul Appell.Efter at have afsluttet sine ph.d. -studier, Padé undervises på Lycée FAIDHERBE i Lille, optage dette indlæg i oktober 1893.
After completing his doctoral studies, Padé taught at the Lycée Faidherbe in Lille, taking up this post in October 1893.I 1889 Padé gik til Tyskland til at fortsætte sine studier, som går først til Leipzig og derefter til Göttingen og studere under Klein og Schwarz.
In 1889 Padé went to Germany to continue his studies, going first to Leipzig and then to Göttingen, studying under Klein and Schwarz.ATTENTION- Automatisk oversættelse fra engelsk version Henri Padé blev født i Abbeville, som er en by nordvest for Amiens i Picardie-regionen i det nordlige Frankrig.
Wikipedia Henri Padé was born in Abbeville which is a town northwest of Amiens in the Picardy region of northern France.Padé havde gjort andre betydelige bidrag dog, såsom forlagsvirksomhed en elementær algebra bog og omsætte Klein's Erlangen programmet fra tysk til fransk.
Padé had made other significant contributions, however, such as publishing an elementary algebra book and translating Klein 's Erlangen programme from German into French.Hvor meget af dette tidligere arbejde var kendt Padé er mindre indlysende og han sikkert syntes at være uvidende af bidragene fra Frobenius.
How much of this earlier work was known to Padé is less obvious and he certainly seemedPadé etableret forskellige egenskaber af denne tabel i sin afhandling og udviklet idéer videre i senere papirer, især i 1899, når han undersøger den eksponentielle serien og i 1901, da han mente(1+ x) m, for mig ikke et heltal.
Padé established various properties of this table in his thesis and developed the ideas further in later papers, particularly in 1899 when he studies the exponential series and in 1901 when he considered(1+x)m, for m not an integer.I januar 1897,lidt over tre år efter optage sin udnævnelse på Lycée FAIDHERBE, Padé blev Maître de Conférences på universitetet i Lille.
In January 1897,a little over three years after taking up his appointment at the Lycée Faidherbe, Padé became Maître de Conférences at the University of Lille.I sin doktordisputats Padé viste, at i et ordentligt defineret forstand, Padé approximant var den bedste approximant blandt alle de fornuftige.
In his doctoral thesis Padé showed that, in a properly defined sense, the Padé approximant was the best approximant among all the rational ones.Den metode, fortsatte med at blive brugt fra tid til anden af forskellige matematikere,f. eks Kummer i 1837 brugt Padé approximants at summen serier som kun konvergerede meget langsomt.
The method continued to be used from time to time by various mathematicians,for example Kummer in 1837 used Padé approximants to sum series which only converged very slowly.I sin afhandling Padé foretaget den første systematiske undersøgelse af, hvad vi kalder i dag Padé approximants, som er rationel tilnærmelser til funktioner givet ved deres magt serien.
In his thesis Padé made the first systematic study of what we call today Padé approximants, which are rational approximations to functions given by their power series.Efter at have opnået høje stående ved universitetet i Bordeaux, Padé venstre universiteter i 1908, da han var 44 år gammel, blev rektor for Akademiet i Besançon.
Having achieved high standing at the University of Bordeaux, Padé left universities in 1908, when he was 44 years old, to became Rector of the Academy in Besançon.Padé's ph.d. -vejleder Hermite havde benyttet approximants ogfortsatte fraktioner i sit arbejde af 1873 om beviser de transcendens af E. Hvor meget af dette tidligere arbejde var kendt Padé er mindre indlysende og han sikkert syntes at være uvidende af bidragene fra Frobenius.
Padé's doctoral supervisor Hermitehad used approximants and continued fractions in his work of 1873 on proving the transcendence of e. How much of this earlier work was known to Padé is less obvious and he certainly seemed Det første der syntes at indse den fulde betydning af metoden for Padé approximants var Lagrange i et papir i 1776, hvor han relateret dem til fortsat fraktioner.
The first who seemed to realise the full significance of the method of Padé approximants was Lagrange in a paper of 1776 where he related them to continued fractions.Fem indlæg blev modtaget og fire dommere er blevet udnævnt, Emile Picard, Painlevé, Poincarés, og Appell. Emile Picard læse to af de redegørelser,herunder den ene af Padé, mens disse andre dommere læse en hver af de resterende tre poster. Brezinski skriver.
Five submissions were received and four referees were appointed, Emile Picard, Painlevé, Poincaré, and Appell. Emile Picard read two of the submissions,including the one by Padé, while these other referees read one each of the remaining three entries. Brezinski writes.Tre af de fem indlæg modtaget en præmie, med Padé modtager første præmien sammen med halvdelen af det samlede pengepræmie, med mindre beløb går til indlæg vurderes at være værdig til andet og tredje sted.
Three of the five submissions received a prize, with Padé receiving the first prize together with half the total prize money, with smaller amounts going to the submissions judged to be worthy of second and third place.I 1892 han præsenterede sin ph.d. -afhandling Sur la repræsentation approchee d'une funktionen par des fraktioner rationelles til Sorbonne i Paris. Padé forsvarede sin afhandling om den 21 juni 1892, eksaminatorer bliver hans vejleder Hermite, sammen med Emile Picard og Paul Appell.
In 1892 he presented his doctoral thesis Sur la representation approchee d'une fonction par des fractions rationelles to the Sorbonne in Paris. Padé defended his thesis on 21 June 1892, the examiners being his supervisor Hermite, together with Emile Picard and Paul Appell.Eksistensen af approximants var naturligvis kendt før Padé, men ingen systematisk undersøgelse af dem havde fundet sted, undtagen ved Frobenius, der bestemmes den vigtige forbindelser, som normalt findes mellem dem.
The existence of approximants was, of course, well-known before Padé, but no systematic examination of them had been made except by Frobenius, who determined the important relations which normally exist between them.
