fschieber/wit-captions huggingface dataset:
xy-圖展示出函數 
  
    
      
        f
        (
        x
        )
        
        
      
    
    {\displaystyle f(x)\,\!}
  
 的勒壤得轉換。函數用紅色表示，在切點 
  
    
      
        (
        
          x
          
            0
          
        
        ,
         
        f
        (
        
          x
          
            0
          
        
        )
        )
        
        
      
    
    {\displaystyle (x_{0},\ f(x_{0}))\,\!}
  
 的切線用藍色表示。切線與 y-軸相交於點 
  
    
      
        (
        0
        ,
         
        −
        
          f
          
            ∗
          
        
        )
        
        
      
    
    {\displaystyle (0,\ -f^{*})\,\!}
  
 ；這裏，
  
    
      
        
          f
          
            ∗
          
        
        
        
      
    
    {\displaystyle f^{*}\,\!}
  
 是勒壤得轉換 
  
    
      
        
          f
          
            ∗
          
        
        (
        
          p
          
            0
          
        
        )
        
        
      
    
    {\displaystyle f^{*}(p_{0})\,\!}
  
 的值，
  
    
      
        
          p
          
            0
          
        
        =
        
          
            
              f
              ˙
            
          
        
        (
        
          x
          
            0
          
        
        )
        
        
      
    
    {\displaystyle p_{0}={\dot {f}}(x_{0})\,\!}
  
 。特別注意，穿過在紅線上任何其它點，而擁有同樣斜率 
  
    
      
        
          
            
              f
              ˙
            
          
        
        (
        
          x
          
            0
          
        
        )
        
        
      
    
    {\displaystyle {\dot {f}}(x_{0})\,\!}
  
 的直線，其與 y-軸相交點必定比點  
  
    
      
        (
        0
        ,
         
        −
        
          f
          
            ∗
          
        
        )
        
        
      
    
    {\displaystyle (0,\ -f^{*})\,\!}
  
 高，證明 
  
    
      
        
          f
          
            ∗
          
        
        
        
      
    
    {\displaystyle f^{*}\,\!}
  
 確實是極大值。
Diagram showing the geometric interpretation of the Legendre transform of the function f(x). The tangent line at x0 intercepts the y axis at f*, which is the value of the Legendre transform for argument p= f'(x0).
Schamanen als „Sachverständige und Vermittler zur Geisterwelt“ nach Klaus E. Müller vor der europäischen Expansion, die im 15. Jahrhundert einsetzte (Farbflächen); sowie traditionelle Schamanen und andere religiös-spirituelle Spezialisten zu Anfang des 21. Jahrhunderts, die noch verschiedene soziale Funktionen innehaben (schwarz-weiße Symbole/Schraffuren)
            Elementarschamanismus Komplexschamanismus Besessenheitsschamanismus ﻿Klassisch (primär), arktische Völker
 ﻿Klassisch (sekundär), Nordsibirien
 ﻿Klassisch, Südostasien*
 ﻿Subarktis Nordamerikas
 ﻿Eingeschränkt, Nordamerika
 ﻿Eingeschränkt, Südamerika
  ﻿Australien ﻿Klassisch westsibirisch
 ﻿Klassisch zentralsibirisch
 ﻿Klassisch altaiisch
 ﻿Klassisch mandschurisch
 ﻿Klassisch südost-asiatisch**
  ﻿Nordosten Nordamerikas
 ﻿Südwesten Nordamerikas
 ﻿Meso- und Südamerika  ﻿Islamischer Einflussbereich
 ﻿Lamaistischer Einflussbereich
 ﻿Buddhistisch-daoistischer Einflussbereich  farbige Kreis-Symbole:
 *) = Weitgehend traditionelle Jäger- u. Sammler innerhalb moderner oder bäuerlicher Gesellschaften
 **) = Weitgehend traditionelle Pflanzer innerhalb moderner oder bäuerlicher Gesellschaften                   Map-icon-circle-black.png Isolierte Ethnien mit komplett erhaltenen sozialen Funktionen ihrer religiös-spirituellen Spezialisten Map-icon-black-question-mark.png Isolierte Ethnien Neuguineas mit traditionellen Religionen, jedoch ohne Kenntnisse über Schamanen o. ä. Geisterbeschwörer Map-icon-circle-black-white.png Lokale Gemeinschaften mit weitgehend intakten traditionellen Strukturen, in denen Geisterbeschwörer noch einige ihrer ursprünglichen Funktionen ausüben. Ihre Funktionen sind jedoch durch moderne Einflüsse bereits mehr oder weniger beeinflusst. Map-icon-Transition-area--hatch-black-white.png Traditionelle Gesellschaften mit weitgehend intakten Strukturen, in denen Geisterbeschwörer noch einige ihrer ursprünglichen Funktionen ausüben (Verbreitungsdichte je nach Schraffur/Flächenfüllung) Map-icon-dotted-area-black.png Traditionell in Staaten u./o. andere Religionen integrierte „Stadtschamanen“ Ost- und Südostasiens
Deutsch: Weltkarte Schamanismus nach Klaus E. Müller um 1500 sowie dokumentierte Beispiele für traditionelle Schamanen und ähnliche Geisterbeschwörer um den Beginn des 21. Jahrhunderts herum
Calcul de la rotation d'angle 
  
    
      
        θ
      
    
    {\displaystyle \theta }
  
 du vecteur 
  
    
      
        
          
            
              O
              A
            
            →
          
        
      
    
    {\displaystyle {\overrightarrow {OA}}}
  
 à l'aide de la matrice de rotation : 

  
    
      
        
          
            (
            
              
                
                  
                    A
                    
                      x
                    
                    ′
                  
                
              
              
                
                  
                    A
                    
                      y
                    
                    ′
                  
                
              
            
            )
          
        
        =
        
          
            (
            
              
                
                  cos
                  ⁡
                  θ
                
                
                  −
                  sin
                  ⁡
                  θ
                
              
              
                
                  sin
                  ⁡
                  θ
                
                
                  cos
                  ⁡
                  θ
                
              
            
            )
          
        
        
          
            (
            
              
                
                  
                    A
                    
                      x
                    
                  
                
              
              
                
                  
                    A
                    
                      y
                    
                  
                
              
            
            )
          
        
      
    
    {\displaystyle {\begin{pmatrix}A'_{x}\\A'_{y}\end{pmatrix}}={\begin{pmatrix}\cos \theta &-\sin \theta \\\sin \theta &\cos \theta \\\end{pmatrix}}{\begin{pmatrix}A_{x}\\A_{y}\end{pmatrix}}}
Español: Rotación de un vector
Desde arriba a la izquierda, en el sentido de las agujas del reloj: la carrera musical de Beethoven despegó y alcanzó su punto máximo en esta época. La década de 1820 fue la década en que Beethoven compuso y publicó su icónica sinfonía No. 9 - ahora parte del Programa Memoria del Mundo de la UNESCO, antes de su muerte en 1827. Hasta la fecha, Beethoven es uno de los músicos más influyentes del mundo, ya que su las composiciones se encuentran entre las partituras musicales más populares en orquestas; la Primera Revolución Industrial alcanza un impulso máximo para Occidente, como se muestra en este grabado de una fábrica textil que opera en Mánchester , posiblemente el centro industrial de Inglaterra del siglo XIX; La fotografía más antigua del mundo que se conserva fue tomada en 1826, como se ve arriba. La década fue el comienzo del desarrollo del daguerrotipo, un instrumento utilizado para la captura de imágenes en movimiento y fue un instrumento precursor de la cámara; Las Guerras de independencia hispanoamericanas estaban en pleno apogeo, ya que países como Brasil, Bolivia, Perú y Uruguay obtuvieron su independencia en esta época, un punto de inflexión para la política regional e influyó fuertemente en las condiciones sociopolíticas contemporáneas de América del Sur; Las multitudes se reúnen para presenciar la apertura del primer ferrocarril del mundo, el ferrocarril de Stockton y Darlington, tal como comenzó formalmente en 1825; El primer motor eléctrico del mundo fue creado por el ingeniero húngaro Ányos Jedlik. Su invento conduciría a formar el conocimiento y la utilización de la electricidad de hoy en día, y una forma forjada para que crezcan los estudios sobre electroquímica e ingeniería; La Antártida fue descubierta y explorada por primera vez. Su expedición inaugural en aguas continentales fue dirigida por una tripulación rusa encabezada por Fabian Gottlieb von Bellingshausen, en 1819 a 1821; La máquina de escribir recibe su primera patente en 1829, un avance en la tecnología y un camino pavimentado para formar las comunicaciones modernas y la informática.
English: A montage of notable events in the 1820s.
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English: Highway shield for Malaysian Federal Route 35
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Geomorphological subdivisions of Dinaric Alps 
 Legend:  
 A1: The area of the North Adriatic - the territory of Istria and the Kras area 
 A2: Northern Adriatic - North Adriatic islands 
 A3: Mountains of Dalmatia - Central mountain range 
 A4: Dalmatian Mountains - Coastal Mountain Range 
 A5: The mountains of southern Dalmatia and Mediterranean Herzegovina 
 A6: The islands of Central and South Adriatic and Peljesac 
 A7: Primorje Mountains of Montenegro 
 A8: Coastal and Central Montenegro Mountains - Katunska karst flattening 
 A9: Mountains of the Montenegrin Rudina 
 A10/11: Mountains of Low Herzegovina 
 B1: Group of Trnova herod 
 B2: Snežnik and Gorski kotar plateaus 
 B3: Notran plateau 
 B4: Great Chapel (Velika Kapela)
 B5: Massive Velebit 
 B6: Little Chapel (Mala Kapela) and Lika Center 
 B7: Massif Lička Plješivica (Plješevica) 
 B8: Massive Dinara 
 B9: Šator 
 B10: Cincar 
 B11: Klekovača (S) and Grmeč (N) 
 B12: Raduša 
 B13: Čvrsnica 
 B14: Massive Prenj 
 B15: High mountains of Herzegovina - Velež and Herzegovinian Rudine 
 B16: Mountains of High Herzegovina - Mountain range of Crvanj-Lebršnik 
 B17: Zelengora Group 
 B18: Bioč-Maglic-Volujak Group 
 B19: Vranica Group 
 B20: Bjelašnica (Southern Sarajevo Mountains) 
 B21: Mountain range Golija-Vojnik 
 B22: Group Switches 
 B23: Durmitor area 
 B24: Sinjajevina 
 B25: The Moravian-Fallen Mountains and Maganik 
 B26: Ljubišnja 
 B27: Massive Bjelasica 
 B28: Komovi 
 B29: Visitor 
 B30: Kučke planine (Žijovo) 
 B31: Albanian Alps 
 C1: Group of Kočevski Rog 
 C2: Žumberak / Gorjanci Group 
 C3: Central and Eastern Bosnia Mountains - Vlašić Group 
 C4: Central Bosnia Mountains 
 C5: Eastern Bosnia Mountains 
 C6: Central and Eastern Bosnia Mountains - Jahorina Group 
 C7: Mountains of Stara Vlaha and Raska (Sandžak) - Polymers-Podrinje Group 
 C8: Mountains of Stara Vlaha and Raška (Sandžak) - Zlatarsko-pešterska Group 
 C9: Mountains of the Old Mountains - the central group 
 C10: Mountains of Serbia - Podrinje-valjevo mountains 
 C11: Pre-Dinaric Mountains: Kozara (NW) och Majevica (SE).
States that allow direct initiated constitutional amendments  States that allow legislatively-referred and direct initiative statutes, or legislatively-referred and direct initiated constitutional amendments or referendums.   States that allow legislatively-referred and indirect initiative statutes, or legislatively-referred and direct initiated constitutional amendments or referendums.   Illinois allows legislatively-referred initiative statutes, or legislatively-referred and direct initiated constitutional amendments or referendums.   Mississippi allows legislatively-referred, indirect, and direct initiated constitutional amendments.   Florida allows legislatively-referred, and direct initiated constitutional amendments. States and federal district that allow initiated statutes   Massachusetts allows legislatively-referred and indirect initiative statutes, or legislatively-referred and indirect initiated constitutional amendments or referendums, with the specific initiative petition term used for all directly-voted initiatives.   States that allow legislatively-referred, indirect, and direct initiative statutes, or legislatively-referred initiated constitutional amendments or referendums.   Idaho allows direct initiative statutes, or legislatively-referred initiated constitutional amendments or referendums.   States that allow indirect initiative statutes, or legislatively-referred initiated constitutional amendments or referendums.   Washington D.C. allows direct initiative statutes. States that allow referendums   States that allow legislatively-referred state statutes, or legislatively-referred initiated constitutional amendments or referendums, or citizen-initiated referendums of existing statutes.   Delaware allows legislatively-referred state statutes or citizen initiated referendums of existing statutes. States that allow legislative referral only   Kentucky allows legislatively-referred state statutes and legislatively-referred initiated constitutional amendments.   States that allow legislatively-referred initiated constitutional amendments only.
Pohoří Turecka:

A – Pontské pohoří: 1 Bolu Dağları, 2 Ilgaz Dağları, 3 Küre Dağları, 4 Canik Dağları, 5 Giresun Dağları, 6 Rize Dağları. Malý Kavkaz: 7 Karçal Dağları, 8 Šavšetský hřbet.

B – Taurus: 9 Akdağlar, 10 Bey Dağları, 11 Yanartaş Dağları, 12 Katrancik Dağları, 13 Kuyucak Dağları, 14 Dedegöl Dağları, 15 Geyık Dağları, 16 Yarımadası, 17 Erenler Dağı, 18 Eşenler Dağı, 19 Oyuklu Dağı, 20 Karaman Platosu, 21 Bolkar Dağları, 22 Ala Dağlar, 23 Dibek Dağları, 24 Binboğa Dağları, 25 Berıt Dağı, 26 Nurhak Dağı, 27 Malatya Dağları, 28 Maden Dağları, 29 Akdağ, 30 Genç Dağları, 31 Bitlis Dağları, 32 İhtiyarşahap Dağları, 33 Yazlıca Dağı, 34 Hakkari Dağları, 35 Koçkıran Dağı

C – Arménská vysočina: 36 Yalnizçam Dağları, 37 Allahuekber Dağları, 38 Mescit Dağları, 39 Otlukbeli Dağları, 40 Esence Dağları, 41 Kargapazarı Dağları, 42 Karasu Aras Dağları, 43 Karagöl Dağları, 44 Körboğa Dağları, 45 Serafettin Dağları, 46 Oltuk Dağları, 47 Akdoğan Dağları, 48 Aladağ, 49 Pirreşit Dağları, 50 Erek Dağı

D – Anatolská plošina a hory západního Turecka: 51 Samanlı Dağları, 52 Katırlı Dağları, 53 Uludağ, 54 Köroğlu Dağları, 55 Sündiken Dağları, 56 Abdüsselam Dağları, 57 Elmadağ, 58 Kervansaray Dağı, 59 Armutçük Dağı, 60 Kaz Dağı, 61 Eğriöz Dağı ,62 Boz Dağları, 63 Aydın Dağları, 64 Beşparmak Dağları, 65 Madranbaba Dağları, 66 Gölgeli Dağ, 67 Sandıklı Dağı ,68 Karakuş Dağı, 69 Sultan Dağları, 70 Buzluk Dağı, 71 Devecı Dağları, 72 Ak Dağlar, 73 Sakabat Dağları, 74 Köse Dağları, 75 Camlıbel Dağları

Pohoří na pomezí Arménské vysočiny, Anatolské plošiny a Tauru: 76 Munzur, 77 Tecer Dağları, 78 Yama Dağı, 79 Tahtalı Dağları. Levantská horstva: 80 Nur Dağları, 81 Kartal Dağı. Balkán: 82 Gelibolu Yarımadası,83 Yıldız Dağları

Sopečné vrcholy: 1 Hasan Dağı, 2 Keçıboydaran, 3 Melendiz Dağı, 4 Erdas Dağı, 5 Hodul Dağı, 6 Erciyes Dağı, 7 Karadağ, 8 Karacadağ, 9 Gökdelen Dağı, 10 Nemrut Dağı, 11 Süphan Dağı, 12 Esrük Dağı, 13 Tendürek Dağı, 14 Ararat, 15 Yağlıca Dağı, 16 Dumanlı Dağı – Tarhandağı, 17 Kısırdağı, 18 Akbaba Dağı, 19 Kel Dağı / Zıyaret, 20 Ilgar Dağı / Uglar, 21 Alem Dağı
Legenda: ██ Granice okruga ██ Granice gradskih kotara        Sjeverna naselja:
 1. Kotar:
  • Čizar
  • Dar-Abad
  • Darake
  • Darband
  • Džamaran
  • Elahije
  • Farmanije
  • Kejtarije
  • Nobonjad
  • Tadžriš
  • Zafaranije
 2. Kotar:
  • Farahzad
  • Giša
  • Punak-e
   Bahtari
  • Sadat-Abad
  • Sadegije
  • Šahrak-e Garb
  • Šahrak-e
   Žandarmeri
  • Tarašt
  • Tovhid
 3. Kotar:
   • Darus
  • Davudije
  • Ehtijarije
  • Golhak
  • Vanak
  • Žordan
 5. Kotar:
  • Bulvar-e
   Firdusi
  • Džanat-Abad
  • Ekbatan
  • Punak
 6. Kotar:
  • Amir-Abad
  • Aržantin
  • Jusef-Abad
  • Park-e Lale
  Istočna naselja:
 4. Kotar:
  • Hak Sefid
  • Hakimije
  • Lavizan
  • Ozgol
  • Pasdaran
  • Resalat
  • Šams-Abad
  • Šemiran No
  • Tehranpars
  • Zargande
 7. Kotar:
  • Abas-Abad
  • Behdžat-
   Abad
  • Imam
   Hosein
  • Sabalan
 8. Kotar:
  • Moalem
  • Narmak
  • Samangan
 13. Kotar:
  • Došan-Tape
  • Niru Havaji
  • Teheran No
 14. Kotar:
  • Čaharsad
   Dastgah
  • Dulab
  • Horasan
  • Isfahanak
  • Sad Dastgah
  Središnja naselja:
 10. Kotar:
  • Berjanak
  • Haft-Čenar
  • Salsabil
 11. Kotar:
  • Dohanijat
  • Laškar
  • Monirije
  • Šejh Hadi
 12. Kotar:
  • Baharestan
  • Bazar-e Tehran
  • Firdusi
  • Gorgan
  • Park-e Šaher
  • Pič-e Šemiran
 17. Kotar:
  • Imamzade
   Hasan
  • Hazane Falah
  • Kale Morgi
  Južna naselja:
 15. Kotar:
  • Afsarije
  • Bisim
  • Havaran
  • Kijanšaher
  • Masudije
  • Moširije
 16. Kotar:
  • Ali-Abad
  • Bag-e Azari
  • Hazane
   Boharae
  • Jahči-Abad
  • Nazi-Abad
 19. Kotar:
  • Abdol-Abad
  • Hava Niruz
  • Nemat-Abad
 20. Kotar:
  • Dovlat-Abad
  • Džavanm-e
   Kasab
  • Ebn-e
   Babavejh
  • Hazrat-e
   Abdol-Azim
  • Sizdah-e
   Aban
  Zapadna naselja:
 9. Kotar:
  • Džej
  • Sar-Asjab
 18. Kotar:
  • Čahar-Bari
  • Jaft-Abad
  • Šad-Abad
  • Šahrak-e
   Vali-Asr
  • Tolid Daru
 21. Kotar:
  • Iran Hodro
  • Tehransar
  • Vardavard
 22. Kotar:
  • Bag-e
   Hadž-Sejf
  • Kan
  • Kuj-e
   Sazman-e
   Barname
  • Čitgar
  • Pejkanšaher
  • Stadium-e
   Azadi
  • Šahrak-e
   Češme
  • Šahrak-e
   Rah-Ahan
English: Tehran municipality (Croatian description)
Lei de Biot-Savart. Um condutor curvo transportando uma corrente i (em azul) é dividido em seções devidamente representadas pelo vetor diferencial de caminho 
  
    
      
        
          
            
              
                d
                s
              
              →
            
          
        
      
    
    {\displaystyle {\vec {ds}}}
  
 (em vermelho). O elemento de corrente 
  
    
      
        i
        
          
            
              
                d
                s
              
              →
            
          
        
      
    
    {\displaystyle i{\vec {ds}}}
  
  (em preto) é representado por um vetor de módulo i vezes maior, na mesma direção e sentido estabelecidos por 
  
    
      
        
          
            
              
                d
                s
              
              →
            
          
        
      
    
    {\displaystyle {\vec {ds}}}
  
. Vê-se também o vetor 
  
    
      
        
          
            
              r
              →
            
          
        
      
    
    {\displaystyle {\vec {r}}}
  
 que localiza o ponto onde calcula-se o campo em relação à seção 
  
    
      
        
          
            
              
                d
                s
              
              →
            
          
        
      
    
    {\displaystyle {\vec {ds}}}
  
 bem como o vetor 
  
    
      
        
          
            
              
                d
                B
              
              →
            
          
        
      
    
    {\displaystyle {\vec {dB}}}
  
 resultante (ambos em preto), este perpendicular tanto a  
  
    
      
        i
        
          
            
              
                d
                s
              
              →
            
          
        
      
    
    {\displaystyle i{\vec {ds}}}
  
 como a 
  
    
      
        
          
            
              r
              →
            
          
        
      
    
    {\displaystyle {\vec {r}}}
  
 .
English: Laplace's formulation of Biot-Savart law