"Eine glatte Funktion ist eine mathematische Funktion, die beliebig oft differenzierbar ist. Die Bezeichnung \u201Eglatt\u201C ist durch die Anschauung motiviert: Der Graph einer glatten Funktion hat keine \u201EEcken\u201C, also Stellen, an denen sie nicht differenzierbar ist. Damit wirkt der Graph \u00FCberall \u201Ebesonders glatt\u201C. Zum Beispiel ist jede holomorphe Funktion auch eine glatte Funktion. Au\u00DFerdem werden glatte Funktionen als Abschneidefunktionen oder als Testfunktionen f\u00FCr Distributionen verwendet."@de . . . . . . . . "\u0646\u0639\u0648\u0645\u0629 \u062F\u0627\u0644\u0629"@ar . . . . . . "\uD574\uC11D\uD559\uC5D0\uC11C \uB9E4\uB044\uB7EC\uC6B4 \uD568\uC218(\uC601\uC5B4: smooth function)\uB294 \uBB34\uD55C \uBC88 \uBBF8\uBD84\uC774 \uAC00\uB2A5\uD55C \uD568\uC218\uC774\uB2E4. \uD568\uC218\uB85C \uD45C\uAE30\uD558\uAE30\uB3C4 \uD55C\uB2E4. \uB9CC\uC57D \uD568\uC218\uAC00 \uB9E4\uB044\uB7FD\uACE0 \uBAA8\uB4E0 \uC810\uC5D0\uC11C\uC758 \uD14C\uC77C\uB7EC \uAE09\uC218 \uAC12\uC774 \uD568\uC218\uAC12\uACFC \uAC19\uC744 \uACBD\uC6B0\uC5D0\uB294 \uD574\uC11D \uD568\uC218\uAC00 \uB41C\uB2E4."@ko . . . . . . . . "\uB9E4\uB044\uB7EC\uC6B4 \uD568\uC218"@ko . . . . . . . . . "In matematica, una funzione liscia in un punto del suo dominio \u00E8 una funzione che \u00E8 differenziabile infinite volte in tale punto, o equivalentemente, che \u00E8 derivabile infinite volte nel punto rispetto ad ogni sua variabile (per il teorema del differenziale totale, infatti, una funzione \u00E8 differenziabile in un punto se le sue derivate parziali sono ivi continue). Se una funzione \u00E8 liscia in tutti i punti di un insieme , si dice che essa \u00E8 di classe su , e si scrive ."@it . . . . . . . . . "Fun\u00E7\u00E3o suave"@pt . . "Eine glatte Funktion ist eine mathematische Funktion, die beliebig oft differenzierbar ist. Die Bezeichnung \u201Eglatt\u201C ist durch die Anschauung motiviert: Der Graph einer glatten Funktion hat keine \u201EEcken\u201C, also Stellen, an denen sie nicht differenzierbar ist. Damit wirkt der Graph \u00FCberall \u201Ebesonders glatt\u201C. Zum Beispiel ist jede holomorphe Funktion auch eine glatte Funktion. Au\u00DFerdem werden glatte Funktionen als Abschneidefunktionen oder als Testfunktionen f\u00FCr Distributionen verwendet."@de . . . . . . . "Glatt funktion"@sv . . . "In matematica, una funzione liscia in un punto del suo dominio \u00E8 una funzione che \u00E8 differenziabile infinite volte in tale punto, o equivalentemente, che \u00E8 derivabile infinite volte nel punto rispetto ad ogni sua variabile (per il teorema del differenziale totale, infatti, una funzione \u00E8 differenziabile in un punto se le sue derivate parziali sono ivi continue). Se una funzione \u00E8 liscia in tutti i punti di un insieme , si dice che essa \u00E8 di classe su , e si scrive ."@it . . . . "Una funci\u00F3n suave o infinitamente diferenciable es una funci\u00F3n que admite derivadas de cualquier orden, y por tanto todas sus derivadas de cualquier orden son continuas. Las funciones anal\u00EDticas son casos particulares de funciones suaves, pero no toda funci\u00F3n suave es anal\u00EDtica. Por ejemplo la funci\u00F3n: Es infinitamente diferenciable en todos sus puntos pero no es anal\u00EDtica. \n* Datos: Q868473"@es . . . . . . . . "1124748591"^^ . . "Smoothness"@en . . . . "Una funci\u00F3n suave o infinitamente diferenciable es una funci\u00F3n que admite derivadas de cualquier orden, y por tanto todas sus derivadas de cualquier orden son continuas. Las funciones anal\u00EDticas son casos particulares de funciones suaves, pero no toda funci\u00F3n suave es anal\u00EDtica. Por ejemplo la funci\u00F3n: Es infinitamente diferenciable en todos sus puntos pero no es anal\u00EDtica. \n* Datos: Q868473"@es . . . . . . . "En glatt funktion, eller sl\u00E4t funktion, \u00E4r en funktion som kan deriveras o\u00E4ndligt m\u00E5nga g\u00E5nger. Varken den glatta funktion eller dess derivator har n\u00E5gra \"h\u00F6rn\", utan kan beskrivas som just sl\u00E4ta. M\u00E4ngden av alla glatta funktioner brukar betecknas C\u221E. Vissa menar att en funktion inte beh\u00F6ver vara o\u00E4ndligt deriverbar f\u00F6r att kallas glatt utan endast tillr\u00E4ckligt m\u00E5nga g\u00E5nger deriverbar f\u00F6r de aktuella syftena. Man kan d\u00E5 s\u00E4ga att funktionen \u00E4r \"tillr\u00E4ckligt glatt\". Funktioner kan ocks\u00E5 vara styckvis glatta. Ett enkelt exempel p\u00E5 detta \u00E4r en vanlig fyrkantsv\u00E5g som \u00E4r glatt \u00F6verallt utom p\u00E5 just de v\u00E4rden d\u00E4r de \"hoppar\". En komplex funktion som \u00E4r differentierbar en g\u00E5ng p\u00E5 en \u00F6ppen m\u00E4ngd \u00E4r ocks\u00E5 b\u00E5de o\u00E4ndligt differentierbar (glatt) och analytisk p\u00E5 denna m\u00E4ngd."@sv . "Funkcja regularna \u2013 funkcja r\u00F3\u017Cniczkowalna okre\u015Blon\u0105 liczb\u0119 razy w swojej dziedzinie. Dok\u0142adniej: Niech b\u0119dzie dana funkcja gdzie oraz Funkcj\u0119 nazywamy funkcj\u0105 regularn\u0105 rz\u0119du na je\u017Celi: \n* wszystkie pochodne cz\u0105stkowe funkcji do rz\u0119du w\u0142\u0105cznie istniej\u0105 w ca\u0142ej dziedzinie \n* pochodne te s\u0105 ci\u0105g\u0142e w ca\u0142ej dziedzinie M\u00F3wimy te\u017C, \u017Ce funkcja jest klasy i piszemy Regularno\u015B\u0107 oznacza, \u017Ce funkcja jest ci\u0105g\u0142a. Funkcj\u0119 nazywa si\u0119 funkcj\u0105 g\u0142adk\u0105; jest ona dowolnie wysokiej regularno\u015Bci, to znaczy istniej\u0105 pochodne wszystkich rz\u0119d\u00F3w i s\u0105 ci\u0105g\u0142e. Ponadto dla klasy funkcji analitycznych stosuje si\u0119 oznaczenie"@pl . . . . "Fonction lisse"@fr . . "\u5149\u6ED1\u51FD\u6570\uFF08\u82F1\u8A9E\uFF1ASmooth function\uFF09\u5728\u6570\u5B66\u4E2D\u7279\u6307\u65E0\u7A77\u53EF\u5BFC\u7684\u51FD\u6570\uFF0C\u4E0D\u5B58\u5728\u5C16\u70B9\uFF0C\u4E5F\u5C31\u662F\u8BF4\u6240\u6709\u7684\u6709\u9650\u9636\u5BFC\u6570\u90FD\u5B58\u5728\u3002\u4F8B\u5982\uFF0C\u6307\u6570\u51FD\u6570\u5C31\u662F\u5149\u6ED1\u7684\uFF0C\u56E0\u4E3A\u6307\u6570\u51FD\u6570\u7684\u5BFC\u6570\u662F\u6307\u6570\u51FD\u6570\u672C\u8EAB\u3002 \u82E5\u4E00\u51FD\u6570\u662F\u8FDE\u7EED\u7684\uFF0C\u5219\u79F0\u5176\u4E3A\u51FD\u6570\uFF1B\u82E5\u51FD\u6570\u5B58\u5728\u5BFC\u51FD\u6570\uFF0C\u4E14\u5176\u5C0E\u51FD\u6578\u9023\u7E8C\uFF0C\u5247\u7A31\u70BA\u8FDE\u7EED\u53EF\u5BFC\uFF0C\u8A18\u4E3A\u51FD\u6570\uFF1B\u82E5\u4E00\u51FD\u6570\u9636\u53EF\u5BFC\uFF0C\u5E76\u4E14\u5176\u9636\u5BFC\u51FD\u6570\u8FDE\u7EED\uFF0C\u5219\u4E3A\u51FD\u6570\uFF08\uFF09\u3002\u800C\u5149\u6ED1\u51FD\u6570\u662F\u5BF9\u6240\u6709\u90FD\u5C5E\u4E8E\u51FD\u6570\uFF0C\u7279\u79F0\u5176\u4E3A\u51FD\u6570\u3002"@zh . . "\u062F\u0631\u062C\u0629 \u0642\u0627\u0628\u0644\u064A\u0629 \u0627\u0644\u0627\u0634\u062A\u0642\u0627\u0642 \u062F\u0627\u0644\u0629 \u0645\u0639\u064A\u0646\u0629 (\u0628\u0627\u0644\u0625\u0646\u062C\u0644\u064A\u0632\u064A\u0629: Differentiability Class)\u200F \u0648\u062A\u0639\u0631\u0641 \u0623\u064A\u0636\u0627 \u0628\u0646\u0639\u0648\u0645\u0629 \u0627\u0644\u062F\u0627\u0644\u0629 (\u0628\u0627\u0644\u0625\u0646\u062C\u0644\u064A\u0632\u064A\u0629: Smoothness)\u060C \u0623\u0648 \u0631\u062A\u0628\u0629 \u0627\u0644\u0627\u0646\u062A\u0638\u0627\u0645 \u0641\u064A \u0627\u0644\u0645\u0631\u0627\u062C\u0639 \u0627\u0644\u0641\u0631\u0646\u0633\u064A\u0629 (Classe de r\u00E9gularit\u00E9)\u060C \u0647\u064A \u062E\u0627\u0635\u064A\u0629 \u0641\u064A \u0627\u0644\u062A\u062D\u0644\u064A\u0644 \u0627\u0644\u0631\u064A\u0627\u0636\u064A \u0644\u0648\u0635\u0641 \u062F\u0648\u0627\u0644 \u062A\u0642\u0628\u0644 \u0627\u0634\u062A\u0642\u0627\u0642\u0627\u062A \u0645\u062A\u062A\u0627\u0644\u064A\u0629 \u0625\u0644\u0649 \u0631\u062A\u0628\u0629 \u0645\u0639\u064A\u0646\u0629 \u0648\u062A\u0643\u0648\u0646 \u0645\u062A\u0635\u0644\u0629. \u0627\u0644\u062F\u0627\u0644\u0629 \u0627\u0644\u062A\u064A \u062A\u062D\u0642\u0642 \u0647\u0630\u0647 \u0627\u0644\u062E\u0627\u0635\u064A\u0629 (\u0625\u0644\u0649 \u0645\u0627 \u0644\u0627\u0646\u0647\u0627\u064A\u0629 \u0645\u0646 \u0627\u0644\u0631\u062A\u0628) \u062A\u0633\u0645\u0649 \u0628\u0627\u0644\u062F\u0627\u0644\u0629 \u0627\u0644\u0646\u0627\u0639\u0645\u0629 \u0648\u0641\u064A \u0627\u0644\u0645\u0631\u0627\u062C\u0639 \u0627\u0644\u0641\u0631\u0646\u0633\u064A\u0629 \u0628\u0627\u0644\u062F\u0627\u0644\u0629 \u0627\u0644\u0645\u0644\u0633\u0627\u0621 \u0623\u0648 \u0627\u0644\u0645\u0646\u062A\u0638\u0645\u0629."@ar . . . . . "\u5149\u6ED1\u51FD\u6570\uFF08\u82F1\u8A9E\uFF1ASmooth function\uFF09\u5728\u6570\u5B66\u4E2D\u7279\u6307\u65E0\u7A77\u53EF\u5BFC\u7684\u51FD\u6570\uFF0C\u4E0D\u5B58\u5728\u5C16\u70B9\uFF0C\u4E5F\u5C31\u662F\u8BF4\u6240\u6709\u7684\u6709\u9650\u9636\u5BFC\u6570\u90FD\u5B58\u5728\u3002\u4F8B\u5982\uFF0C\u6307\u6570\u51FD\u6570\u5C31\u662F\u5149\u6ED1\u7684\uFF0C\u56E0\u4E3A\u6307\u6570\u51FD\u6570\u7684\u5BFC\u6570\u662F\u6307\u6570\u51FD\u6570\u672C\u8EAB\u3002 \u82E5\u4E00\u51FD\u6570\u662F\u8FDE\u7EED\u7684\uFF0C\u5219\u79F0\u5176\u4E3A\u51FD\u6570\uFF1B\u82E5\u51FD\u6570\u5B58\u5728\u5BFC\u51FD\u6570\uFF0C\u4E14\u5176\u5C0E\u51FD\u6578\u9023\u7E8C\uFF0C\u5247\u7A31\u70BA\u8FDE\u7EED\u53EF\u5BFC\uFF0C\u8A18\u4E3A\u51FD\u6570\uFF1B\u82E5\u4E00\u51FD\u6570\u9636\u53EF\u5BFC\uFF0C\u5E76\u4E14\u5176\u9636\u5BFC\u51FD\u6570\u8FDE\u7EED\uFF0C\u5219\u4E3A\u51FD\u6570\uFF08\uFF09\u3002\u800C\u5149\u6ED1\u51FD\u6570\u662F\u5BF9\u6240\u6709\u90FD\u5C5E\u4E8E\u51FD\u6570\uFF0C\u7279\u79F0\u5176\u4E3A\u51FD\u6570\u3002"@zh . "\uD574\uC11D\uD559\uC5D0\uC11C \uB9E4\uB044\uB7EC\uC6B4 \uD568\uC218(\uC601\uC5B4: smooth function)\uB294 \uBB34\uD55C \uBC88 \uBBF8\uBD84\uC774 \uAC00\uB2A5\uD55C \uD568\uC218\uC774\uB2E4. \uD568\uC218\uB85C \uD45C\uAE30\uD558\uAE30\uB3C4 \uD55C\uB2E4. \uB9CC\uC57D \uD568\uC218\uAC00 \uB9E4\uB044\uB7FD\uACE0 \uBAA8\uB4E0 \uC810\uC5D0\uC11C\uC758 \uD14C\uC77C\uB7EC \uAE09\uC218 \uAC12\uC774 \uD568\uC218\uAC12\uACFC \uAC19\uC744 \uACBD\uC6B0\uC5D0\uB294 \uD574\uC11D \uD568\uC218\uAC00 \uB41C\uB2E4."@ko . . . . "In de analyse is een gladde functie een functie die oneindig vaak (willekeurig vaak) differentieerbaar is. Een gladde functie behoort daarmee tot de hoogste differentieerbaarheidsklasse, . Het woord glad doelt op het gladde, zeer gelijkmatige verloop van de grafiek van zo'n functie."@nl . . . . "Funkcja regularna"@pl . . . . . . "In mathematical analysis, the smoothness of a function is a property measured by the number of continuous derivatives it has over some domain, called differentiability class. At the very minimum, a function could be considered smooth if it is differentiable everywhere (hence continuous). At the other end, it might also possess derivatives of all orders in its domain, in which case it is said to be infinitely differentiable and referred to as a C-infinity function (or function)."@en . "1408000"^^ . "Na an\u00E1lise matem\u00E1tica e topologia diferencial, as classes de diferenciabilidade s\u00E3o fam\u00EDlias de fun\u00E7\u00F5es com certas propriedades quanto \u00E0 sua continuidade e de suas derivadas. A classe das fun\u00E7\u00F5es suaves corresponde \u00E0quelas fun\u00E7\u00F5es que possuem derivadas de todas as ordens."@pt . . . . . "Gladde functie"@nl . . . . . . . . . . . . . . "Glatte Funktion"@de . . . "Na an\u00E1lise matem\u00E1tica e topologia diferencial, as classes de diferenciabilidade s\u00E3o fam\u00EDlias de fun\u00E7\u00F5es com certas propriedades quanto \u00E0 sua continuidade e de suas derivadas. A classe das fun\u00E7\u00F5es suaves corresponde \u00E0quelas fun\u00E7\u00F5es que possuem derivadas de todas as ordens."@pt . . . . . . . . "In de analyse is een gladde functie een functie die oneindig vaak (willekeurig vaak) differentieerbaar is. Een gladde functie behoort daarmee tot de hoogste differentieerbaarheidsklasse, . Het woord glad doelt op het gladde, zeer gelijkmatige verloop van de grafiek van zo'n functie."@nl . . . . "Funci\u00F3n infinitamente diferenciable"@es . "In mathematical analysis, the smoothness of a function is a property measured by the number of continuous derivatives it has over some domain, called differentiability class. At the very minimum, a function could be considered smooth if it is differentiable everywhere (hence continuous). At the other end, it might also possess derivatives of all orders in its domain, in which case it is said to be infinitely differentiable and referred to as a C-infinity function (or function)."@en . "En glatt funktion, eller sl\u00E4t funktion, \u00E4r en funktion som kan deriveras o\u00E4ndligt m\u00E5nga g\u00E5nger. Varken den glatta funktion eller dess derivator har n\u00E5gra \"h\u00F6rn\", utan kan beskrivas som just sl\u00E4ta. M\u00E4ngden av alla glatta funktioner brukar betecknas C\u221E. Vissa menar att en funktion inte beh\u00F6ver vara o\u00E4ndligt deriverbar f\u00F6r att kallas glatt utan endast tillr\u00E4ckligt m\u00E5nga g\u00E5nger deriverbar f\u00F6r de aktuella syftena. Man kan d\u00E5 s\u00E4ga att funktionen \u00E4r \"tillr\u00E4ckligt glatt\"."@sv . . "\u6ED1\u3089\u304B\u306A\u95A2\u6570"@ja . . . . . . "Funkcja regularna \u2013 funkcja r\u00F3\u017Cniczkowalna okre\u015Blon\u0105 liczb\u0119 razy w swojej dziedzinie. Dok\u0142adniej: Niech b\u0119dzie dana funkcja gdzie oraz Funkcj\u0119 nazywamy funkcj\u0105 regularn\u0105 rz\u0119du na je\u017Celi: \n* wszystkie pochodne cz\u0105stkowe funkcji do rz\u0119du w\u0142\u0105cznie istniej\u0105 w ca\u0142ej dziedzinie \n* pochodne te s\u0105 ci\u0105g\u0142e w ca\u0142ej dziedzinie M\u00F3wimy te\u017C, \u017Ce funkcja jest klasy i piszemy"@pl . . . . . . . . . . . "\u6570\u5B66\u306B\u304A\u3044\u3066\u3001\u95A2\u6570\u306E\u6ED1\u3089\u304B\u3055\uFF08\u306A\u3081\u3089\u304B\u3055\u3001\u82F1: smoothness\uFF09\u306F\u3001\u305D\u306E\u95A2\u6570\u306B\u5BFE\u3057\u3066\u5FAE\u5206\u53EF\u80FD\u6027\u3092\u8003\u3048\u308B\u3053\u3068\u3067\u6E2C\u3089\u308C\u308B\u3002\u3088\u308A\u9AD8\u3044\u968E\u6570\u306E\u5C0E\u95A2\u6570\u3092\u6301\u3064\u95A2\u6570\u307B\u3069\u6ED1\u3089\u304B\u3055\u306E\u5EA6\u5408\u3044\u304C\u5F37\u3044\u3068\u8003\u3048\u3089\u308C\u308B\u3002 \u76F4\u89B3\u7684\u306B\u306F\u3001\u30B0\u30E9\u30D5\u306E\u5404\u70B9\u3092\u3069\u3093\u306A\u306B\u62E1\u5927\u3057\u3066\u3082\u5C16\u3063\u3066\u3044\u306A\u3044\u3053\u3068\u3092\u610F\u5473\u3059\u308B\u3002"@ja . . "Funzione liscia"@it . . . . "27107"^^ . . . . . . . . . . . . . . . . . "\u6570\u5B66\u306B\u304A\u3044\u3066\u3001\u95A2\u6570\u306E\u6ED1\u3089\u304B\u3055\uFF08\u306A\u3081\u3089\u304B\u3055\u3001\u82F1: smoothness\uFF09\u306F\u3001\u305D\u306E\u95A2\u6570\u306B\u5BFE\u3057\u3066\u5FAE\u5206\u53EF\u80FD\u6027\u3092\u8003\u3048\u308B\u3053\u3068\u3067\u6E2C\u3089\u308C\u308B\u3002\u3088\u308A\u9AD8\u3044\u968E\u6570\u306E\u5C0E\u95A2\u6570\u3092\u6301\u3064\u95A2\u6570\u307B\u3069\u6ED1\u3089\u304B\u3055\u306E\u5EA6\u5408\u3044\u304C\u5F37\u3044\u3068\u8003\u3048\u3089\u308C\u308B\u3002 \u76F4\u89B3\u7684\u306B\u306F\u3001\u30B0\u30E9\u30D5\u306E\u5404\u70B9\u3092\u3069\u3093\u306A\u306B\u62E1\u5927\u3057\u3066\u3082\u5C16\u3063\u3066\u3044\u306A\u3044\u3053\u3068\u3092\u610F\u5473\u3059\u308B\u3002"@ja . . "\u062F\u0631\u062C\u0629 \u0642\u0627\u0628\u0644\u064A\u0629 \u0627\u0644\u0627\u0634\u062A\u0642\u0627\u0642 \u062F\u0627\u0644\u0629 \u0645\u0639\u064A\u0646\u0629 (\u0628\u0627\u0644\u0625\u0646\u062C\u0644\u064A\u0632\u064A\u0629: Differentiability Class)\u200F \u0648\u062A\u0639\u0631\u0641 \u0623\u064A\u0636\u0627 \u0628\u0646\u0639\u0648\u0645\u0629 \u0627\u0644\u062F\u0627\u0644\u0629 (\u0628\u0627\u0644\u0625\u0646\u062C\u0644\u064A\u0632\u064A\u0629: Smoothness)\u060C \u0623\u0648 \u0631\u062A\u0628\u0629 \u0627\u0644\u0627\u0646\u062A\u0638\u0627\u0645 \u0641\u064A \u0627\u0644\u0645\u0631\u0627\u062C\u0639 \u0627\u0644\u0641\u0631\u0646\u0633\u064A\u0629 (Classe de r\u00E9gularit\u00E9)\u060C \u0647\u064A \u062E\u0627\u0635\u064A\u0629 \u0641\u064A \u0627\u0644\u062A\u062D\u0644\u064A\u0644 \u0627\u0644\u0631\u064A\u0627\u0636\u064A \u0644\u0648\u0635\u0641 \u062F\u0648\u0627\u0644 \u062A\u0642\u0628\u0644 \u0627\u0634\u062A\u0642\u0627\u0642\u0627\u062A \u0645\u062A\u062A\u0627\u0644\u064A\u0629 \u0625\u0644\u0649 \u0631\u062A\u0628\u0629 \u0645\u0639\u064A\u0646\u0629 \u0648\u062A\u0643\u0648\u0646 \u0645\u062A\u0635\u0644\u0629. \u0627\u0644\u062F\u0627\u0644\u0629 \u0627\u0644\u062A\u064A \u062A\u062D\u0642\u0642 \u0647\u0630\u0647 \u0627\u0644\u062E\u0627\u0635\u064A\u0629 (\u0625\u0644\u0649 \u0645\u0627 \u0644\u0627\u0646\u0647\u0627\u064A\u0629 \u0645\u0646 \u0627\u0644\u0631\u062A\u0628) \u062A\u0633\u0645\u0649 \u0628\u0627\u0644\u062F\u0627\u0644\u0629 \u0627\u0644\u0646\u0627\u0639\u0645\u0629 \u0648\u0641\u064A \u0627\u0644\u0645\u0631\u0627\u062C\u0639 \u0627\u0644\u0641\u0631\u0646\u0633\u064A\u0629 \u0628\u0627\u0644\u062F\u0627\u0644\u0629 \u0627\u0644\u0645\u0644\u0633\u0627\u0621 \u0623\u0648 \u0627\u0644\u0645\u0646\u062A\u0638\u0645\u0629."@ar . . . "\u5149\u6ED1\u51FD\u6570"@zh . . . .