Symmetry of second derivatives

en

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Symmetry of second derivatives

Quality:

Symmetry of second derivatives - theorem. Article "Symmetry of second derivatives" in English Wikipedia has 51.5 points for quality (as of November 1, 2023). The article contains 43 references and 12 sections.

In this language version of Wikipedia the article has the best quality. Also, this article is the most popular in that language version.

In October 2023 the article "Symmetry of second derivatives" was edited by 1 authors in English Wikipedia and written by 1 authors in all languages.

Since the creation of article "Symmetry of second derivatives", its content was written by 103 registered users of English Wikipedia and edited by 307 registered Wikipedia users in all languages.

The article is cited 64 times in English Wikipedia and cited 407 times in all languages.

The highest Authors Interest rank from 2001:

  • Local (English): #8534 in August 2020
  • Global: #27709 in September 2004

The highest popularity rank from 2008:

  • Local (English): #153361 in October 2020
  • Global: #117199 in October 2019

There are 15 language versions for this article in the WikiRank database (of the considered 55 Wikipedia language editions).

The quality and popularity assessment was based on Wikipédia dumps from November 1, 2023 (including revision history and pageviews for previous years).

下表顯示了最高品質的文章的語言版本。

Languages with the highest quality

#LanguageQuality gradeQuality score
1English (en)
Symmetry of second derivatives
51.544
2German (de)
Satz von Schwarz
21.7747
3Chinese (zh)
二阶导数的对称性
21.2858
4French (fr)
Théorème de Schwarz
19.8622
5Indonesian (id)
Simetri turunan kedua
14.7126
6Arabic (ar)
مبرهنة شفارز
14.4573
7Russian (ru)
Равенство смешанных производных
13.526
8Polish (pl)
Twierdzenie Schwarza
12.2855
9Italian (it)
Teorema di Schwarz
11.2733
10Japanese (ja)
ヤングの定理
10.4622
More...

The following table shows the most popular language versions of the article.

Most popular in all the time

The most popular language versions of the article "Symmetry of second derivatives" in all the time
#LanguagePopularity awardRelative popularity
1English (en)
Symmetry of second derivatives
768 623
2German (de)
Satz von Schwarz
414 223
3Italian (it)
Teorema di Schwarz
278 909
4French (fr)
Théorème de Schwarz
222 836
5Spanish (es)
Teorema de Clairaut
204 128
6Russian (ru)
Равенство смешанных производных
74 738
7Polish (pl)
Twierdzenie Schwarza
65 008
8Chinese (zh)
二阶导数的对称性
56 970
9Portuguese (pt)
Teorema de Clairaut-Schwarz
53 925
10Japanese (ja)
ヤングの定理
23 647
More...

The following table shows the language versions of the article with the highest popularity in the last month.

Most popular in October 2023

The most popular language versions of the article "Symmetry of second derivatives" in October 2023
#LanguagePopularity awardRelative popularity
1English (en)
Symmetry of second derivatives
7 383
2German (de)
Satz von Schwarz
2 251
3French (fr)
Théorème de Schwarz
1 872
4Italian (it)
Teorema di Schwarz
1 328
5Spanish (es)
Teorema de Clairaut
1 304
6Russian (ru)
Равенство смешанных производных
524
7Chinese (zh)
二阶导数的对称性
395
8Portuguese (pt)
Teorema de Clairaut-Schwarz
255
9Polish (pl)
Twierdzenie Schwarza
152
10Japanese (ja)
ヤングの定理
138
More...

The following table shows the language versions of the article with the highest Authors’ Interest.

The highest AI

Language versions of the article "Symmetry of second derivatives" with the highest Authors Interest (number of authors). Only registered Wikipedia users were taken into account.
#LanguageAI awardRelative AI
1English (en)
Symmetry of second derivatives
103
2German (de)
Satz von Schwarz
44
3French (fr)
Théorème de Schwarz
35
4Italian (it)
Teorema di Schwarz
34
5Spanish (es)
Teorema de Clairaut
17
6Chinese (zh)
二阶导数的对称性
14
7Catalan (ca)
Teorema de Clairaut
10
8Danish (da)
Clairauts sætning
10
9Japanese (ja)
ヤングの定理
10
10Russian (ru)
Равенство смешанных производных
10
More...

The following table shows the language versions of the article with the highest Authors’ Interest in the last month.

The highest AI in October 2023

Language versions of the article "Symmetry of second derivatives" with the highest AI in October 2023
#LanguageAI awardRelative AI
1English (en)
Symmetry of second derivatives
1
2Arabic (ar)
مبرهنة شفارز
0
3Catalan (ca)
Teorema de Clairaut
0
4Danish (da)
Clairauts sætning
0
5German (de)
Satz von Schwarz
0
6Spanish (es)
Teorema de Clairaut
0
7French (fr)
Théorème de Schwarz
0
8Indonesian (id)
Simetri turunan kedua
0
9Italian (it)
Teorema di Schwarz
0
10Japanese (ja)
ヤングの定理
0
More...

The following table shows the language versions of the article with the highest number of citations.

The highest CI

Language versions of the article "Symmetry of second derivatives" with the highest Citation Index (CI)
#LanguageCI awardRelative CI
1Chinese (zh)
二阶导数的对称性
100
2English (en)
Symmetry of second derivatives
64
3Polish (pl)
Twierdzenie Schwarza
47
4French (fr)
Théorème de Schwarz
45
5German (de)
Satz von Schwarz
30
6Italian (it)
Teorema di Schwarz
24
7Japanese (ja)
ヤングの定理
23
8Spanish (es)
Teorema de Clairaut
19
9Portuguese (pt)
Teorema de Clairaut-Schwarz
17
10Catalan (ca)
Teorema de Clairaut
16
More...

Scores

Estimated value for Wikipedia:
English:
Global:
Popularity in October 2023:
English:
Global:
Popularity in all years:
English:
Global:
Authors in October 2023:
English:
Global:
Registered authors in all years:
English:
Global:
Citations:
English:
Global:

Quality measures

Interwikis

#LanguageValue
arArabic
مبرهنة شفارز
caCatalan
Teorema de Clairaut
daDanish
Clairauts sætning
deGerman
Satz von Schwarz
enEnglish
Symmetry of second derivatives
esSpanish
Teorema de Clairaut
frFrench
Théorème de Schwarz
idIndonesian
Simetri turunan kedua
itItalian
Teorema di Schwarz
jaJapanese
ヤングの定理
plPolish
Twierdzenie Schwarza
ptPortuguese
Teorema de Clairaut-Schwarz
roRomanian
Simetria derivatei a doua
ruRussian
Равенство смешанных производных
zhChinese
二阶导数的对称性

Popularity rank trends

Best Rank English:
#153361
10.2020
Global:
#117199
10.2019

AI rank trends

Best Rank English:
#8534
08.2020
Global:
#27709
09.2004

Local AI rank history

Languages comparison

Important global interconnections

Wikipedia readers most often find their way to information on Symmetry of second derivatives from Wikipedia articles about Partial derivative, Hessian matrix, Maxwell relations, Fubinis theorem and Exact differential equation. Whereas reading the article about Symmetry of second derivatives people most often go to Wikipedia articles on Hermann Schwarz, Hessian matrix, Schwarz lemma, Alexis Clairaut and Greens theorem.

Cumulative results of quality and popularity of the Wikipedia article

List of Wikipedia articles in different languages (starting with the most popular):

News from 11 June 2024

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In English Wikipedia the most popular articles on that day were: Mohan Charan Majhi, Hunter Biden, ChatGPT, 2026 FIFA World Cup qualification (AFC), Chirag Paswan, Deaths in 2024, 2024 Indian general election, UEFA Euro 2024, 2024 ICC Men's T20 World Cup, Hit Man (2023 film).

About WikiRank

The WikiRank project is intended for automatic relative evaluation of the articles in the various language versions of Wikipedia. At the moment the service allows to compare over 44 million Wikipedia articles in 55 languages. Quality scores of articles are based on Wikipedia dumps from November, 2023. When calculating current popularity and AI of articles data from October 2023 was taken into account. For historical values of popularity and AI WikiRank used data from 2001 to 2023... More information