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About: Smoothness
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endpoint"><i class="bi-box-arrow-up-right"></i> Sparql Endpoint </a> </li> </ul> </div> </div> </nav> <div style="margin-bottom: 60px"></div> <!-- /navbar --> <!-- page-header --> <section> <div class="container-xl"> <div class="row"> <div class="col"> <h1 id="title" class="display-6"><b>About:</b> <a href="http://dbpedia.org/resource/Smoothness">Smoothness</a> </h1> </div> </div> <div class="row"> <div class="col"> <div class="text-muted"> <span class="text-nowrap">An Entity of Type: <a href="http://dbpedia.org/ontology/Building">building</a>, </span> <span class="text-nowrap">from Named Graph: <a href="http://dbpedia.org">http://dbpedia.org</a>, </span> <span class="text-nowrap">within Data Space: <a href="http://dbpedia.org">dbpedia.org</a></span> </div> </div> </div> <div class="row pt-2"> <div class="col-xs-9 col-sm-10"> <p class="lead">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).</p> </div> <div class="col-xs-3 col-sm-2"> <a href="#" class="thumbnail"> <img src="http://commons.wikimedia.org/wiki/Special:FilePath/Bump2D_illustration.png?width=300" alt="thumbnail" class="img-fluid" /> </a> </div> </div> </div> </section> <!-- page-header --> <!-- property-table --> <section> <div class="container-xl"> <div class="row"> <div class="table-responsive"> <table class="table table-hover table-sm table-light"> <thead> <tr> <th class="col-xs-3 ">Property</th> <th class="col-xs-9 px-3">Value</th> </tr> </thead> <tbody> <tr class="odd"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/abstract"><small>dbo:</small>abstract</a> </td><td class="col-10 text-break"><ul> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="ar" >درجة قابلية الاشتقاق دالة معينة (بالإنجليزية: Differentiability Class) وتعرف أيضا بنعومة الدالة (بالإنجليزية: Smoothness)، أو رتبة الانتظام في المراجع الفرنسية (Classe de régularité)، هي خاصية في التحليل الرياضي لوصف دوال تقبل اشتقاقات متتالية إلى رتبة معينة وتكون متصلة. الدالة التي تحقق هذه الخاصية (إلى ما لانهاية من الرتب) تسمى بالدالة الناعمة وفي المراجع الفرنسية بالدالة الملساء أو المنتظمة.</span><small> (ar)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="de" >Eine glatte Funktion ist eine mathematische Funktion, die beliebig oft differenzierbar ist. Die Bezeichnung „glatt“ ist durch die Anschauung motiviert: Der Graph einer glatten Funktion hat keine „Ecken“, also Stellen, an denen sie nicht differenzierbar ist. Damit wirkt der Graph überall „besonders glatt“. Zum Beispiel ist jede holomorphe Funktion auch eine glatte Funktion. Außerdem werden glatte Funktionen als Abschneidefunktionen oder als Testfunktionen für Distributionen verwendet.</span><small> (de)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="es" >Una función suave o infinitamente diferenciable es una función que admite derivadas de cualquier orden, y por tanto todas sus derivadas de cualquier orden son continuas. Las funciones analíticas son casos particulares de funciones suaves, pero no toda función suave es analítica. Por ejemplo la función: Es infinitamente diferenciable en todos sus puntos pero no es analítica. * Datos: Q868473</span><small> (es)</small></span></li> <li><span class="literal"><span property="dbo:abstract" lang="en" >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).</span><small> (en)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="it" >In matematica, una funzione liscia in un punto del suo dominio è una funzione che è differenziabile infinite volte in tale punto, o equivalentemente, che è derivabile infinite volte nel punto rispetto ad ogni sua variabile (per il teorema del differenziale totale, infatti, una funzione è differenziabile in un punto se le sue derivate parziali sono ivi continue). Se una funzione è liscia in tutti i punti di un insieme , si dice che essa è di classe su , e si scrive .</span><small> (it)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="ja" >数学において、関数の滑らかさ（なめらかさ、英: smoothness）は、その関数に対して微分可能性を考えることで測られる。より高い階数の導関数を持つ関数ほど滑らかさの度合いが強いと考えられる。 直観的には、グラフの各点をどんなに拡大しても尖っていないことを意味する。</span><small> (ja)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="ko" >해석학에서 매끄러운 함수(영어: smooth function)는 무한 번 미분이 가능한 함수이다. 함수로 표기하기도 한다. 만약 함수가 매끄럽고 모든 점에서의 테일러 급수 값이 함수값과 같을 경우에는 해석 함수가 된다.</span><small> (ko)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="nl" >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.</span><small> (nl)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="pl" >Funkcja regularna – funkcja różniczkowalna określoną liczbę razy w swojej dziedzinie. Dokładniej: Niech będzie dana funkcja gdzie oraz Funkcję nazywamy funkcją regularną rzędu na jeżeli: * wszystkie pochodne cząstkowe funkcji do rzędu włącznie istnieją w całej dziedzinie * pochodne te są ciągłe w całej dziedzinie Mówimy też, że funkcja jest klasy i piszemy Regularność oznacza, że funkcja jest ciągła. Funkcję nazywa się funkcją gładką; jest ona dowolnie wysokiej regularności, to znaczy istnieją pochodne wszystkich rzędów i są ciągłe. Ponadto dla klasy funkcji analitycznych stosuje się oznaczenie</span><small> (pl)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="sv" >En glatt funktion, eller slät funktion, är en funktion som kan deriveras oändligt många gånger. Varken den glatta funktion eller dess derivator har några "hörn", utan kan beskrivas som just släta. Mängden av alla glatta funktioner brukar betecknas C∞. Vissa menar att en funktion inte behöver vara oändligt deriverbar för att kallas glatt utan endast tillräckligt många gånger deriverbar för de aktuella syftena. Man kan då säga att funktionen är "tillräckligt glatt". Funktioner kan också vara styckvis glatta. Ett enkelt exempel på detta är en vanlig fyrkantsvåg som är glatt överallt utom på just de värden där de "hoppar". En komplex funktion som är differentierbar en gång på en öppen mängd är också både oändligt differentierbar (glatt) och analytisk på denna mängd.</span><small> (sv)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="pt" >Na análise matemática e topologia diferencial, as classes de diferenciabilidade são famílias de funções com certas propriedades quanto à sua continuidade e de suas derivadas. A classe das funções suaves corresponde àquelas funções que possuem derivadas de todas as ordens.</span><small> (pt)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="zh" >光滑函数（英語：Smooth function）在数学中特指无穷可导的函数，不存在尖点，也就是说所有的有限阶导数都存在。例如，指数函数就是光滑的，因为指数函数的导数是指数函数本身。 若一函数是连续的，则称其为函数；若函数存在导函数，且其導函數連續，則稱為连续可导，記为函数；若一函数阶可导，并且其阶导函数连续，则为函数（）。而光滑函数是对所有都属于函数，特称其为函数。</span><small> (zh)</small></span></li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/thumbnail"><small>dbo:</small>thumbnail</a> </td><td class="col-10 text-break"><ul> <li><span class="literal"><a class="uri" rel="dbo:thumbnail" resource="http://commons.wikimedia.org/wiki/Special:FilePath/Bump2D_illustration.png?width=300" href="http://commons.wikimedia.org/wiki/Special:FilePath/Bump2D_illustration.png?width=300"><small>wiki-commons</small>:Special:FilePath/Bump2D_illustration.png?width=300</a></span></li> </ul></td></tr><tr 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href="http://dbpedia.org/class/yago/Structure104341686"><small>yago</small>:Structure104341686</a></span></li> <li><span class="literal"><a class="uri" rel="rdf:type" resource="http://dbpedia.org/class/yago/Whole100003553" href="http://dbpedia.org/class/yago/Whole100003553"><small>yago</small>:Whole100003553</a></span></li> <li><span class="literal"><a class="uri" rel="rdf:type" resource="http://dbpedia.org/class/yago/WikicatDifferentialStructures" href="http://dbpedia.org/class/yago/WikicatDifferentialStructures"><small>yago</small>:WikicatDifferentialStructures</a></span></li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" href="http://www.w3.org/2000/01/rdf-schema#comment"><small>rdfs:</small>comment</a> </td><td class="col-10 text-break"><ul> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="ar" >درجة قابلية الاشتقاق دالة معينة (بالإنجليزية: Differentiability Class) وتعرف أيضا بنعومة الدالة (بالإنجليزية: Smoothness)، أو رتبة الانتظام في المراجع الفرنسية (Classe de régularité)، هي خاصية في التحليل الرياضي لوصف دوال تقبل اشتقاقات متتالية إلى رتبة معينة وتكون متصلة. الدالة التي تحقق هذه الخاصية (إلى ما لانهاية من الرتب) تسمى بالدالة الناعمة وفي المراجع الفرنسية بالدالة الملساء أو المنتظمة.</span><small> (ar)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="de" >Eine glatte Funktion ist eine mathematische Funktion, die beliebig oft differenzierbar ist. Die Bezeichnung „glatt“ ist durch die Anschauung motiviert: Der Graph einer glatten Funktion hat keine „Ecken“, also Stellen, an denen sie nicht differenzierbar ist. Damit wirkt der Graph überall „besonders glatt“. Zum Beispiel ist jede holomorphe Funktion auch eine glatte Funktion. Außerdem werden glatte Funktionen als Abschneidefunktionen oder als Testfunktionen für Distributionen verwendet.</span><small> (de)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="es" >Una función suave o infinitamente diferenciable es una función que admite derivadas de cualquier orden, y por tanto todas sus derivadas de cualquier orden son continuas. Las funciones analíticas son casos particulares de funciones suaves, pero no toda función suave es analítica. Por ejemplo la función: Es infinitamente diferenciable en todos sus puntos pero no es analítica. * Datos: Q868473</span><small> (es)</small></span></li> <li><span class="literal"><span property="rdfs:comment" lang="en" >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).</span><small> (en)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="it" >In matematica, una funzione liscia in un punto del suo dominio è una funzione che è differenziabile infinite volte in tale punto, o equivalentemente, che è derivabile infinite volte nel punto rispetto ad ogni sua variabile (per il teorema del differenziale totale, infatti, una funzione è differenziabile in un punto se le sue derivate parziali sono ivi continue). Se una funzione è liscia in tutti i punti di un insieme , si dice che essa è di classe su , e si scrive .</span><small> (it)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="ja" >数学において、関数の滑らかさ（なめらかさ、英: smoothness）は、その関数に対して微分可能性を考えることで測られる。より高い階数の導関数を持つ関数ほど滑らかさの度合いが強いと考えられる。 直観的には、グラフの各点をどんなに拡大しても尖っていないことを意味する。</span><small> (ja)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="ko" >해석학에서 매끄러운 함수(영어: smooth function)는 무한 번 미분이 가능한 함수이다. 함수로 표기하기도 한다. 만약 함수가 매끄럽고 모든 점에서의 테일러 급수 값이 함수값과 같을 경우에는 해석 함수가 된다.</span><small> (ko)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="nl" >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.</span><small> (nl)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="pt" >Na análise matemática e topologia diferencial, as classes de diferenciabilidade são famílias de funções com certas propriedades quanto à sua continuidade e de suas derivadas. A classe das funções suaves corresponde àquelas funções que possuem derivadas de todas as ordens.</span><small> (pt)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="zh" >光滑函数（英語：Smooth function）在数学中特指无穷可导的函数，不存在尖点，也就是说所有的有限阶导数都存在。例如，指数函数就是光滑的，因为指数函数的导数是指数函数本身。 若一函数是连续的，则称其为函数；若函数存在导函数，且其導函數連續，則稱為连续可导，記为函数；若一函数阶可导，并且其阶导函数连续，则为函数（）。而光滑函数是对所有都属于函数，特称其为函数。</span><small> (zh)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="pl" >Funkcja regularna – funkcja różniczkowalna określoną liczbę razy w swojej dziedzinie. Dokładniej: Niech będzie dana funkcja gdzie oraz Funkcję nazywamy funkcją regularną rzędu na jeżeli: * wszystkie pochodne cząstkowe funkcji do rzędu włącznie istnieją w całej dziedzinie * pochodne te są ciągłe w całej dziedzinie Mówimy też, że funkcja jest klasy i piszemy</span><small> (pl)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="sv" >En glatt funktion, eller slät funktion, är en funktion som kan deriveras oändligt många gånger. Varken den glatta funktion eller dess derivator har några "hörn", utan kan beskrivas som just släta. Mängden av alla glatta funktioner brukar betecknas C∞. Vissa menar att en funktion inte behöver vara oändligt deriverbar för att kallas glatt utan endast tillräckligt många gånger deriverbar för de aktuella syftena. Man kan då säga att funktionen är "tillräckligt glatt".</span><small> (sv)</small></span></li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://www.w3.org/2000/01/rdf-schema#label"><small>rdfs:</small>label</a> </td><td class="col-10 text-break"><ul> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="ar" >نعومة دالة</span><small> (ar)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="de" >Glatte Funktion</span><small> (de)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="es" >Función infinitamente diferenciable</span><small> (es)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="fr" >Fonction lisse</span><small> (fr)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="it" >Funzione liscia</span><small> (it)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="ko" >매끄러운 함수</span><small> (ko)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="ja" >滑らかな関数</span><small> (ja)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="nl" >Gladde functie</span><small> (nl)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="pl" >Funkcja regularna</span><small> (pl)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="pt" >Função suave</span><small> (pt)</small></span></li> <li><span class="literal"><span property="rdfs:label" lang="en" >Smoothness</span><small> (en)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="sv" >Glatt funktion</span><small> (sv)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="zh" >光滑函数</span><small> (zh)</small></span></li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" href="http://www.w3.org/2002/07/owl#sameAs"><small>owl:</small>sameAs</a> </td><td class="col-10 text-break"><ul> <li><span class="literal"><a class="uri" rel="owl:sameAs" resource="http://rdf.freebase.com/ns/m.01qqxg" href="http://rdf.freebase.com/ns/m.01qqxg"><small>freebase</small>:Smoothness</a></span></li> <li><span class="literal"><a class="uri" rel="owl:sameAs" resource="http://rdf.freebase.com/ns/m.06ngpp" href="http://rdf.freebase.com/ns/m.06ngpp"><small>freebase</small>:Smoothness</a></span></li> <li><span class="literal"><a class="uri" rel="owl:sameAs" resource="http://www.wikidata.org/entity/Q868473" href="http://www.wikidata.org/entity/Q868473"><small>wikidata</small>:Smoothness</a></span></li> <li><span class="literal"><a class="uri" rel="owl:sameAs" 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