Eksempler på brug af Differential operators på Engelsk og deres oversættelser til Dansk
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On adjoint linear differential operators.
På adjoint lineær differentiale operatører.These differential operators became known as'Newcomb operators. .
Disse differentierede operatører blev kendt som'Newcomb operatører«.Stated a number of problems about differential operators.
Anført en række problemer omkring differentierede operatører.He defined differential operators of arbitrary order Dt.
Han definerede forskellen operatører af vilkårlig rækkefølge D t.Volume 2 contains Bott's papers on differential operators.
Bind 2 indeholder Bott's papirer om differentieret operatører.He defined differential operators of arbitrary order D t.
Han definerede forskellen operatører af vilkårlig rækkefølge D t.In his book on distributions Laurent Schwartz… stated a number of problems about differential operators.
I sin bog om distributioner Laurent Schwartz… anført en række problemer omkring differentierede operatører.He had written the book Linear differential operators two years earlier in 1954.
Han havde skrevet bogen Linear differentieret operatører to år tidligere i 1954.Petryshyn in describes other work of Marchenko including his work on self adjoint differential operators.
Petryshyn i beskriver andet arbejde af Marchenko herunder hans arbejde med selvstændige adjoint differentieret operatører.His major treatise on Pseudo Differential Operators was published in Japanese in 1974.
Hans store afhandling om Pseudo Differential Operators blev offentliggjort i Japan i 1974.In these papers a special role is played by expansions in terms of the eigenfunctions of linear differential operators.
I disse papirer en særlig rolle spilles af udvidelser i form af eigenfunctions af lineære differentieret operatører.The problem is that the order of approximation of differential operators in the general case decreases.
Problemet er, at rækkefølgen af tilnærmelse af differentiale operatører i det generelle tilfælde falder.It is also worth separately mentioning the problem of the adaptive mesh application to finite approximation of differential operators.
Det er også værd at nævne separat problemet med adaptive mesh ansøgning til finite tilnærmelse af differentiale operatører.This work updates his original book Linear Partial Differential Operators(1963) which contained the results which led to his award of the Fields Medal.
Dette arbejde opdateringer hans oprindelige bog Lineær partiel Differential Operators(1963), som indeholdt de resultater, som førte til hans tildeling af Fields medaljen.His many fundamental contributions in topology and differential geometry andtheir application to Lie groups, differential operators and mathematical physics.
Hans mange grundlæggende bidrag i topologi og differentieret geometri ogderes anvendelse på Lie grupper, differentiale operatører og matematisk fysik.Formal properties of differential operators are studied in many of his contributions, in particular in his early papers he worked on commuting differential operators.
Formel egenskaber differentieret operatører er undersøgt i mange af hans bidrag, især i hans tidlige papirer han arbejdede på pendling differentieret operatører.Therefore, to solve the Darcy equation,numerical methods such as finite-difference approximation of differential operators and the finite element method are used.
Derfor, at løse Darcy ligning,numeriske metoder såsom finite-forskel tilnærmelse af differentiale operatører og finite element metoden anvendes.He defined differential operators of arbitrary order Dt. Usually t is an integer but in this theory developed by Liouville in papers between 1832 and 1837, t could be a rational, an irrational or most generally of all a complex number.
Han definerede forskellen operatører af vilkårlig rækkefølge D t. Normalt t er et heltal, men i denne teori er udviklet af Liouville i papirer mellem 1832 og 1837, t kunne være en rationel, en irrationel eller de fleste generelt af alle et komplekst tal.The Wolf Prize was awarded:… his many fundamental contributions in topology and differential geometry andtheir application to Lie groups, differential operators and mathematical physics.
De Wolf-prisen blev tildelt:… hans mange grundlæggende bidrag i topologi og differentieret geometri ogderes anvendelse på Lie grupper, differentiale operatører og matematisk fysik.In particular Calderón wanted to describe a calculus for elliptic differential operators and, from this beginning in the 1950s, the theory of pseudodifferential operators grew in the 1960s.
Især Calderón ønskede at beskrive en calculus for elliptisk differentieret operatører og fra denne begyndelse i 1950'erne, teorien om pseudodifferential Newcomb showed how to extend Laplace 's series to give a perturbing function in the case of elliptical orbits by introducing differential operators which act on the Laplace coefficients.
Newcomb viste, hvordan man kan udvide Laplace's serier for at give et perturbing funktion i tilfælde af elliptiske baner ved at indføre differentieret erhvervsdrivende, som handler om Laplace koefficienter.Marchenko made significant contributions to the theory of self-adjoint differential operators with infinitely many independent variables and also to the theory of spaces of functions of infinitely many variables as inductive limits of locally convex function spaces.
Marchenko gjort betydelige bidrag til teorien om selvregulering adjoint differentieret operatører med uendeligt mange uafhængige variabler og også til den teori om rum af funktioner af uendelig mange variabler som induktive grænser af lokalt konvekse funktion mellemrum.In particular he describes how the main areas developed which are covered by his four volume text The analysis of linear partial differential operators the volumes of which appeared between 1983 and 1985.
Især han beskriver, hvordan de vigtigste områder udvikles som er omfattet af hans fire mængde tekst Analysen af lineære partielle differentiale operatører de mængder, der syntes mellem 1983 og 1985.After five years devoted to writing a four volume monograph on linear partial differential operators, I spent the academic years 1984-86 as director of the Mittag-Leffler Institute in Stockholm. I had only accepted a two year appointment with leave of absence from Lund since I suspected that the many administrative duties there would not agree very well with me.
Efter fem år afsat til at skrive en fire volumen monografi om lineære partielle differentiale operatører, jeg har tilbragt det akademiske år 1984-86 som direktør for Mittag-Leffler Instituttet i Stockholm. Jeg havde kun accepteret en to-årig ansættelse med orlov fra Lund da jeg formodede, at de mange administrative opgaver, der ikke ville enes rigtig godt med mig.Frank's most influential papers were probably those concerned with the analytical perturbation of operators on Banach spaces andhis studies on the essential spectrum of certain singular elliptic differential operators.
Frank's mest indflydelsesrige papirer var sandsynligvis dem der vedrører de analytiske forstyrrelse af aktørerne på Banachrum oghans undersøgelser af de væsentlige spektrum af bestemte ental elliptisk differentieret operatører.He continues:… in a lecture in 1945[ Petrovsky]explicitly asked for a general theory of linear differential operators including those which do not appear in the mathematical models of physics.
Han fortsætter:… i en forelæsning i 1945[Petrovsky]udtrykkeligt anmodede om en generel teori om lineær differentiale operatører, herunder dem, der ikke vises i matematiske modeller i fysik.The coefficients in the series were known as'Laplace coefficients' but the drawback of the method was that it only worked for circular orbits.Newcomb showed how to extend Laplace 's series to give a perturbing function in the case of elliptical orbits by introducing differential operators which act on the Laplace coefficients.
Koefficienterne i serien var kendt som'Laplace koefficienter', men den ulempe ved metoden var, at det kun arbejdet for cirkulær kredsløbene.Newcomb viste, hvordan man kan udvide Laplace's serier for at give et perturbing funktion i tilfælde af elliptiske baner ved at indføre differentieret erhvervsdrivende, som handler om Laplace koefficienter.After five years devoted to writing a four volume monograph on linear partial differential operators, I spent the academic years 1984-86 as director of the Mittag-Leffler Institute in Stockholm.
Efter fem år afsat til at skrive en fire volumen monografi om lineære partielle differentiale operatører, jeg har tilbragt det akademiske år 1984-86 som direktør for Mittag-Leffler Instituttet i Stockholm.Hörmander describes in the later stages of his career:After five years devoted to writing a four volume monograph on linear partial differential operators, I spent the academic years 1984-86 as director of the Mittag-Leffler Institute in Stockholm.
Hörmander beskrives i de senere faser af hans karriere:Efter fem år afsat til at skrive en fire volumen monografi om lineære partielle differentiale operatører, jeg har tilbragt det akademiske år 1984-86 som direktør for Mittag-Leffler Instituttet i Stockholm.Petryshyn in describes other work of Marchenko including his work on self adjoint differential operators: Marchenko made significant contributions to the theory of self-adjoint differential operators with infinitely many independent variables and also to the theory of spaces of functions of infinitely many variables as inductive limits of locally convex function spaces.
Petryshyn i beskriver andet arbejde af Marchenko herunder hans arbejde med selvstændige adjoint differentieret operatører: Marchenko gjort betydelige bidrag til teorien om selvregulering adjoint differentieret operatører med uendeligt mange uafhængige variabler og også til den teori om rum af funktioner af uendelig mange variabler som induktive grænser af lokalt konvekse funktion mellemrum.
