Eksempler på brug af Diophantine equations på Engelsk og deres oversættelser til Dansk
{-}
-
Colloquial
-
Official
-
Medicine
-
Financial
-
Ecclesiastic
-
Official/political
-
Computer
This was awarded for his work on Diophantine equations.
After further papers on Diophantine equations and Diophantine approximation he wrote a series of five papers on Some metrical theorems in Diophantine approximation.
Efter yderligere papirer om Diophantine ligninger og Among other problems studied by Seki were Diophantine equations.
Blandt andre problemer studeret ved Seki blev Diophantine ligninger.Diophantine equations, carrying a history of more than one thousand years, was, until the early years of this century, little more than a collection of isolated problems subjected to ingenious ad hoc methods.
Diophantine ligninger, der transporterer en historie på mere end tusind år, var indtil de første år af dette århundrede, kun lidt mere end en samling af isolerede problemer underkastes geniale ad hoc-metoder.His contributions to the theory of Diophantine equations are discussed in.
Hans bidrag til teorien om Diophantine ligninger er drøftet i.These are: Approximation of algebraic numbers by rationals andapplications thereof to Diophantine equations.
Disse er: Harmonisering af algebraiske tal ved rationals oganvendelser deraf til Diophantine ligninger.Skolem was remarkably productive publishing around 180 papers on topics such as Diophantine equations, mathematical logic, group theory, lattice theory and set theory.
Skolem var bemærkelsesværdigt produktive udgivelse omkring 180 papirer om emner såsom Diophantine ligninger, matematisk logik, gruppe-teori, lattice teori og sæt teorien.For the second edition of the text published in 1984, Grosswald had added material on L-functions and primes in arithmetic progressions,the arithmetic of number fields, and Diophantine equations.
For den anden udgave af teksten blev offentliggjort i 1984, Grosswald havde tilføjet materiale på L-funktioner og primtal i aritmetiske progressions,aritmetiske i antal felter, og Diophantine ligninger.In fact Thue wrote 35 papers on number theory,mostly on the theory of Diophantine equations, and these are reproduced in.
Faktisk Thue skrev 35 papirer om talteori,som oftest i teorien om Diophantine ligninger, og disse er gengivet i.Hilbert in 1900 posed the problem of finding a method for solving Diophantine equations as the 10th problem on his famous list of 23 problems which he believed should be the major challenges for mathematical research this century.
Hilbert i 1900 rejste problemet med at finde en metode til at løse Diophantine ligninger som 10 th problem med hans berømte liste over de 23 problemer, som han mente burde være de store udfordringer for den matematiske forskning i dette århundrede.At this time he was particularly fascinated by solving Diophantine equations.
På dette tidspunkt han var særlig fascineret af løsningen Diophantine ligninger.At the most advanced level he wrote a monograph Analytic methods for Diophantine equations and Diophantine inequalities(1962) which includes many of his contributions extending the Hardy- Littlewood method.
På det mest avancerede niveau, han skrev en monografi analytiske metoder til Diophantine ligninger og It was A Thue who made the breakthrough to general results by proving in 1909 that all Diophantine equations of the form.
Det var en Thue der gjorde gennembrud til generelle resultater ved at bevise, i 1909, at alle Diophantine ligninger af formen.In 1971 at a conference in Bucharest Robinson gave a lecture Solving diophantine equations in which she set the agenda for continuing to study Diophantine equations following the negative solution to Hilbert 's Tenth Problem problem.
I 1971 på en konference i Bukarest Robinson gav en forelæsning Løser diophantine ligninger, hvor hun satte dagsordenen for fortsat at studere Diophantine ligninger efter de negative løsning på Hilbert's tiende Problem problem.He couldn't check each possible method andmaybe there were very involved methods that didn't seem to have anything to do with Diophantine equations but still worked.
Han kunne ikke kontrollere hver mulig metode ogmåske der var meget involveret metoder, der ikke synes at have noget at gøre med Diophantine ligninger, men stadig fungeret.In addition Poinsot worked on number theory andon this topic he studied Diophantine equations, how to express numbers as the difference of two squares and primitive roots.
Ud Poinsot arbejdet på talteori ogpå dette emne han studerede Diophantine ligninger, hvordan man kan udtrykke numre som forskellen på to kvadrater og primitive rødder.In addition Poinsot worked on number theory andon this topic he studied Diophantine equations, how to express numbers as the difference of two squares and primitive roots. However he is best known for his dedication to geometry and, together with Monge, he contributed to the topic regaining its leading role in mathematical research in France in the eighteenth century.
Ud Poinsot arbejdet på talteori ogpå dette emne han studerede Diophantine ligninger, hvordan man kan udtrykke numre som forskellen på to kvadrater og primitive rødder. Men han er bedst kendt for sit engagement i geometri og sammen med Monge, han bidrog til emnet genvinde sin ledende rolle i matematiske forskning i Frankrig i det attende århundrede.The last part of the book describes Alan Baker 's work on linear forms in the logarithms of algebraic numbers and its applications to Diophantine equations and to the determination of imaginary quadratic fields with class number 1 or 2.
Den sidste del af bogen beskriver, Alan Baker's arbejde med lineære former i de logaritme af algebraisk tal og dets applikationer til Diophantine ligninger og til bestemmelse af imaginære kvadratiske felter med klasse nummer 1 eller 2.This is described by Turán in,who first gives the historical setting:[Diophantine equations], carrying a history of more than one thousand years, was, until the early years of this century, little more than a collection of isolated problems subjected to ingenious ad hoc methods.
Dette er beskrevet af Turán,der første giver den historiske indstilling:[Diophantine ligninger], der transporterer en historie på mere end tusind år, var indtil de første år af dette århundrede, kun lidt mere end en samling af isolerede problemer underkastes geniale ad hoc-metoder.These include his improvement of Thue 's theorem, described above, given in his 1920 dissertation, andits application to certain polynomial Diophantine equations in two unknowns, proving an affine curve of genus at least 1 over a number field has only a finite number of integral points in 1929.
Disse omfatter hans forbedring af Thue's sætning, som er beskrevet ovenfor,gives i hans 1920 afhandling, og dens anvendelse til visse polynomiel Diophantine ligninger med to ubekendte, der beviser en Affine kurve af slægten mindst 1 over en række område har kun et begrænset antal integrerende punkter i 1929.It was A Thue who made the breakthrough to general results by proving in 1909 that all Diophantine equations of the form f(x, y) m where m is an integer and f is an irreducible homogeneous binary form of degree at least three, with integer coefficients, have at most finitely many solutions in integers.
Det var en Thue der gjorde gennembrud til generelle resultater ved at bevise, i 1909, at alle Diophantine ligninger af formen f(x, y) m hvor m er et heltal, og f er en irreducible homogene binær form af grad mindst tre, med heltal koefficienter, har allerhøjst finitely mange løsninger i heltal.Let us quote Robinson's own description of the problem which she wrote in an article intended for a general audience in 1975:Hilbert in 1900 posed the problem of finding a method for solving Diophantine equations as the 10th problem on his famous list of 23 problems which he believed should be the major challenges for mathematical research this century.
Lad os citere Robinson's egen beskrivelse af problemet, som hun skrev i en artikel beregnet til et generelt publikum i 1975:Hilbert i 1900 rejste problemet med at finde en metode til at løse Diophantine ligninger som 10 th problem med hans berømte liste over de 23 problemer, som han mente burde være de store udfordringer for den matematiske forskning i dette århundrede.Turán goes on to say that Carl Siegel andKlaus Roth generalised the classes of Diophantine equations for which these conclusions would hold and even bounded the number of solutions.
Turán siger videre, at Carl Siegel ogKlaus Roth generelle klassificering af Diophantine ligninger, for hvilke disse konklusioner ville besidde og endda afgrænset antallet af løsninger.Brouncker gave a method of solving the diophantine equation.
Brouncker gav en metode til at løse Diofantisk ligning.Find an effective way to determine whether a Diophantine equation is soluble.
Finde en effektiv måde at afgøre, om en Diofantisk ligning er opløselig.Instead of asking whether a given Diophantine equation has a solution, ask"for what equations do known methods yield the answer?
I stedet for at spørge, om en given Diofantisk ligning har en løsning, spørg"for, hvad ligninger gøre kendte metoder giver svaret?Robinson was awarded a doctorate in 1948 and that same year started work on Hilbert 's Tenth Problem:find an effective way to determine whether a Diophantine equation is soluble.
Robinson blev tildelt en doktorgrad i 1948 og samme år begyndte arbejdet med Hilbert's tiende Problem:finde en effektiv måde at afgøre, om en Diofantisk ligning er opløselig.The answer lies in a branch of mathematics called recursion theory which was developed during the 1930s by several mathematicians: Church, Gödel, Kleene, Post in the United States, Herbrand in France, Turing in England, Markov in the USSR, etc.The method of proof is based on the fact that there is a Diophantine equation say P(x, y, z,…,w) 0 such that the sets of all values of x in all solutions of P 0 is too complicated a set to be calculated by any method whatever.
Svaret ligger i en gren af matematik kaldes rekursion teori som blev udviklet i løbet af 1930 er af flere matematikere: Church, Gödel, Kleene, Post i USA, Herbrand i Frankrig, Turing i England, Markov i USSR,etc. metode til dokumentation er baseret på det faktum, at der er en Diofantisk ligning sige P(x, y, z,…, w) 0 sådan, at det sæt af alle værdier af x i alle opløsninger af P 0 er for kompliceret et sæt skal beregnes ved enhver metode hvilke.
