Опукле спряження

uk

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Опукле спряження

Quality:

Convex conjugate - the ("dual") lower-semicontinuous convex function resulting from the Legendre–Fenchel transformation of a "primal" function. Article "Опукле спряження" in Ukrainian Wikipedia has 27.6 points for quality (as of July 1, 2025). The article contains 6 references and 18 sections.

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

Since the creation of article "Опукле спряження", its content was written by 1 registered users of Ukrainian Wikipedia and edited by 103 registered Wikipedia users in all languages.

The article is cited 7 times in Ukrainian Wikipedia and cited 288 times in all languages.

The highest Authors Interest rank from 2001:

  • Local (Ukrainian): #83071 in November 2022
  • Global: #134728 in April 2019

The highest popularity rank from 2008:

  • Local (Ukrainian): #283982 in April 2022
  • Global: #319993 in July 2014

There are 9 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 July 1, 2025 (including revision history and pageviews for previous years).

The table below shows the language versions of the article with the highest quality.

Languages with the highest quality

#LanguageQuality gradeQuality score
1English (en)
Convex conjugate
29.905
2Japanese (ja)
凸共役性
29.7276
3Ukrainian (uk)
Опукле спряження
27.5908
4Russian (ru)
Выпуклое сопряжение
22.2468
5Chinese (zh)
凸共轭
14.4017
6French (fr)
Fonction conjuguée
13.1925
7Turkish (tr)
Dışbükey eşlenik
9.3646
8Spanish (es)
Conjugada convexa
8.3982
9Persian (fa)
تابع مزدوج محدب
2.9309
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 "Опукле спряження" in all the time
#LanguagePopularity awardRelative popularity
1English (en)
Convex conjugate
605 263
2French (fr)
Fonction conjuguée
59 973
3Spanish (es)
Conjugada convexa
32 020
4Japanese (ja)
凸共役性
18 977
5Chinese (zh)
凸共轭
15 727
6Russian (ru)
Выпуклое сопряжение
4 438
7Persian (fa)
تابع مزدوج محدب
3 195
8Ukrainian (uk)
Опукле спряження
206
9Turkish (tr)
Dışbükey eşlenik
36
More...

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

Most popular in June 2025

The most popular language versions of the article "Опукле спряження" in June 2025
#LanguagePopularity awardRelative popularity
1English (en)
Convex conjugate
3 073
2French (fr)
Fonction conjuguée
250
3Japanese (ja)
凸共役性
220
4Chinese (zh)
凸共轭
61
5Russian (ru)
Выпуклое сопряжение
59
6Spanish (es)
Conjugada convexa
47
7Turkish (tr)
Dışbükey eşlenik
10
8Ukrainian (uk)
Опукле спряження
8
9Persian (fa)
تابع مزدوج محدب
7
More...

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

The highest AI

Language versions of the article "Опукле спряження" with the highest Authors Interest (number of authors). Only registered Wikipedia users were taken into account.
#LanguageAI awardRelative AI
1English (en)
Convex conjugate
61
2French (fr)
Fonction conjuguée
14
3Japanese (ja)
凸共役性
8
4Russian (ru)
Выпуклое сопряжение
6
5Chinese (zh)
凸共轭
6
6Spanish (es)
Conjugada convexa
3
7Persian (fa)
تابع مزدوج محدب
3
8Turkish (tr)
Dışbükey eşlenik
1
9Ukrainian (uk)
Опукле спряження
1
More...

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

The highest AI in June 2025

Language versions of the article "Опукле спряження" with the highest AI in June 2025
#LanguageAI awardRelative AI
1English (en)
Convex conjugate
0
2Spanish (es)
Conjugada convexa
0
3Persian (fa)
تابع مزدوج محدب
0
4French (fr)
Fonction conjuguée
0
5Japanese (ja)
凸共役性
0
6Russian (ru)
Выпуклое сопряжение
0
7Turkish (tr)
Dışbükey eşlenik
0
8Ukrainian (uk)
Опукле спряження
0
9Chinese (zh)
凸共轭
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 "Опукле спряження" with the highest Citation Index (CI)
#LanguageCI awardRelative CI
1English (en)
Convex conjugate
197
2French (fr)
Fonction conjuguée
33
3Japanese (ja)
凸共役性
15
4Persian (fa)
تابع مزدوج محدب
14
5Chinese (zh)
凸共轭
10
6Russian (ru)
Выпуклое сопряжение
7
7Ukrainian (uk)
Опукле спряження
7
8Spanish (es)
Conjugada convexa
3
9Turkish (tr)
Dışbükey eşlenik
2
More...

Scores

Estimated value for Wikipedia:
Ukrainian:
Global:
Popularity in June 2025:
Ukrainian:
Global:
Popularity in all years:
Ukrainian:
Global:
Authors in June 2025:
Ukrainian:
Global:
Registered authors in all years:
Ukrainian:
Global:
Citations:
Ukrainian:
Global:

Quality measures

Interwikis

#LanguageValue
enEnglish
Convex conjugate
esSpanish
Conjugada convexa
faPersian
تابع مزدوج محدب
frFrench
Fonction conjuguée
jaJapanese
凸共役性
ruRussian
Выпуклое сопряжение
trTurkish
Dışbükey eşlenik
ukUkrainian
Опукле спряження
zhChinese
凸共轭

Popularity rank trends

Best Rank Ukrainian:
#283982
04.2022
Global:
#319993
07.2014

AI rank trends

Best Rank Ukrainian:
#83071
11.2022
Global:
#134728
04.2019

Languages comparison

Important global interconnections

Wikipedia readers most often find their way to information on Convex conjugate from Wikipedia articles about Legendre transformation, Duality, Fenchels duality theorem, Youngs inequality and Fenchel–Moreau theorem. Whereas reading the article about Convex conjugate people most often go to Wikipedia articles on Legendre transformation, Duality, Fenchels duality theorem, Dual space and Fenchel–Moreau 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 8 July 2025

On 8 July 2025 in multilingual Wikipedia, Internet users most often read articles on the following topics: Diogo Jota, João Pedro, Ozzy Osbourne, Laura Siegemund, Aryna Sabalenka, Julian McMahon, Jurassic World Rebirth, 2025 FIFA Club World Cup, Amanda Anisimova, F1.

In Ukrainian Wikipedia the most popular articles on that day were: Х-47М2 «Кинджал», Стефанішина Ольга Віталіївна, Гринцевич Назарій Андрійович, Озерне (селище, Житомирський район), Діогу Жота, МіГ-31, Старовойт Роман Володимирович, Україна, Оззі Осборн, Labubu.

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 July, 2025. When calculating current popularity and AI of articles data from June 2025 was taken into account. For historical values of popularity and AI WikiRank used data from 2001 to 2025... More information