fschieber/wit-captions huggingface dataset:
ਉਦਾਹਰਨ : ਦੋ ਅਯਾਮਾਂ ਵਿੱਚ ਜੜੀ ਇੱਕ ਤਿੰਨ ਅਯਾਮੀ ਗੇਂਦ ਦਾ ਇੱਕ ਚੱਕਰ ਦੇ ਨਾਲ ਨਾਲ ਸਮਾਂਤਰ ਵਿਸਥਾਪਨ। ਨਿਰਦੇਸ਼ਾਂਕਾਂ  
  
    
      
        
          z
          
            1
          
        
      
    
    {\displaystyle z^{1}}
  
 ਅਤੇ 
  
    
      
        
          z
          
            2
          
        
      
    
    {\displaystyle z^{2}}
  
   ਰਾਹੀਂ ਵਿਸ਼ੇਸ਼ ਤੌਰ ਤੇ ਦਰਸਾਈ ਗਈ ਇੱਕ 2-ਅਯਾਮੀ ਸਪੇਸ ਵਿੱਚ ਜੜਿਆ ਇੱਕ ਚੱਕਰ ਜਿਸਦਾ ਅਰਧਵਿਆਸ r ਹੈ। ਦੋ ਅਯਾਮੀ ਸਿਸਟਮ ਅੰਦਰ ਨਿਰਦੇਸ਼ਾਂਕਾਂ  
  
    
      
        
          y
          
            1
          
        
      
    
    {\displaystyle y^{1}}
  
 ਅਤੇ 
  
    
      
        
          y
          
            2
          
        
      
    
    {\displaystyle y^{2}}
  
  ਰਾਹੀਂ ਚੱਕਰ ਅਪਣੇ ਆਪ ਵਿੱਚ ਵਿਸ਼ੇਸ਼ ਤੌਰ ਤੇ ਦਰਸਾਇਆ ਜਾਂਦਾ ਹੈ। ਚੱਕਰ ਅਪਣੇ ਆਪ ਵਿੱਚ ਇੱਕ-ਅਯਾਮੀ ਹੈ ਅਤੇ ਇਸਦੀ ਚਾਪ ਲੰਬਾਈ x ਰਾਹੀਂ ਦਰਸਾਇਆ ਜਾ ਸਕਦਾ ਹੈ। ਨਿਰਦੇਸ਼ਾਂਕ y ਨਿਰਦੇਸ਼ਾਂਕ x ਨਾਲ  
  
    
      
        
          y
          
            1
          
        
        =
        r
        cos
        ⁡
        (
        x
        
          /
        
        r
        )
      
    
    {\displaystyle y^{1}=r\cos(x/r)}
  
 ਅਤੇ 
  
    
      
        
          y
          
            2
          
        
        =
        r
        sin
        ⁡
        (
        x
        
          /
        
        r
        )
      
    
    {\displaystyle y^{2}=r\sin(x/r)}
  
  ਸਬੰਧ ਰਾਹੀਂ ਸਬੰਧਿਤ ਹੁੰਦਾ ਹੈ।  ਇਹ   
  
    
      
        ∂
        
          y
          
            1
          
        
        
          /
        
        ∂
        x
        =
        −
        sin
        ⁡
        (
        x
        
          /
        
        r
        )
      
    
    {\displaystyle \partial y^{1}/\partial x=-\sin(x/r)}
  
 ਅਤੇ  
  
    
      
        ∂
        
          y
          
            2
          
        
        
          /
        
        ∂
        x
        =
        cos
        ⁡
        (
        x
        
          /
        
        r
        )
        .
      
    
    {\displaystyle \partial y^{2}/\partial x=\cos(x/r).}
  
   ਦਿੰਦਾ ਹੈ। ਇਸ ਮਾਮਲੇ ਵਿੱਚ ਮੀਟ੍ਰਿਕ ਸਕੇਲਰ ਹੈ ਅਤੇ   
  
    
      
        g
        =
        
          cos
          
            2
          
        
        ⁡
        (
        x
        
          /
        
        r
        )
        +
        
          sin
          
            2
          
        
        ⁡
        (
        x
        
          /
        
        r
        )
        =
        1.
      
    
    {\displaystyle g=\cos ^{2}(x/r)+\sin ^{2}(x/r)=1.}
  
  ਰਾਹੀਂ ਮਿਲਦਾ ਹੈ। ਫੇਰ ਅੰਤਰਾਲ  
  
    
      
        d
        
          s
          
            2
          
        
        =
        g
        
        d
        
          x
          
            2
          
        
        =
        d
        
          x
          
            2
          
        
        .
        
      
    
    {\displaystyle ds^{2}=g\,dx^{2}=dx^{2}.\,}
  
  ਹੁੰਦਾ ਹੈ। ਅੰਤਰਾਲ ਸਿਰਫ ਚਾਪ ਲੰਬਾਈ ਸਮਾਨ ਹੀ ਹੁੰਦਾ ਹੈ, ਜਿਵੇਂ ਕਿ ਉਮੀਦ ਕੀਤੀ ਜਾਂਦੀ ਹੈ।
Figure 5: Genomic context scheme of Smr45C and its closest homologues in other organisms. The αr45 RNA genes are represented by red arrows and the flanking ORFs by arrows on different colors depending on their product function (legend). Numbers indicate the αr45 RNA gene's and flanking ORFs coordinates in each organism genome database. The gene strand is represented with the file direction. On the left of the figure identification names are used which correspond to a certain organism: αr45_Smr45C = Sinorhizobium meliloti 1021 (NC_003047), αr45_Smedr45C = Sinorhizobium medicae WSM419 chromosome (NC_009636), αr45_Sfr45C = Sinorhizobium fredii NGR234 chromosome (NC_012587), αr45_Atr45C = Agrobacterium tumefaciens str. C58 chromosome linear (NC_003063), αr45_ReCIATr45C = Rhizobium etli CIAT 652 (NC_010994), αr45_Arr45C = Agrobacterium radiobacter K84 chromosome 1 (NC_011985), αr45_Rlt2304r45C = Rhizobium leguminosarum bv. trifolii WSM2304 (NC_011369), αr45_Avr45C = Agrobacterium vitis S4 chromosome 1 (NC_011989), αr45_Rlvr45C = Rhizobium leguminosarum bv. viciae 3841 (NC_008380), αr45_Rlt1325r45C = Rhizobium leguminosarum bv. trifolii WSM1325 (NC_012850), αr45_ReCFNr45C = Rhizobium etli CFN 42 (NC_007761), αr45_Mlr45C = Mesorhizobium loti MAFF303099 chromosome (NC_002678), αr45_Mcr45C = Mesorhizobium ciceri biovar biserrulae WSM1271 chromosome (NC_014923), αr45_Bcr45CII = Brucella canis ATCC 23365 chromosome II (NC_010104), αr45_Bs23445r45CII = Brucella suis ATCC 23445 chromosome II (NC_010167), αr45_Bm16Mr45CII = Brucella melitensis bv. 1 str. 16M chromosome II (NC_003318), αr45_BaS19r45CII = Brucella abortus S19 chromosome 2 (NC_010740), αr45_Bm23457r45CII = Brucella melitensis ATCC 23457 chromosome II (NC_012442), αr45_Bs1330r45CII = Brucella suis 1330 chromosome II (NC_004311), αr45_Ba19941r45CII = Brucella abortus bv. 1 str. 9-941 chromosome II (NC_006933), αr45_Bmar45CII = Brucella melitensis biovar Abortus 2308 chromosome II (NC_007624), αr45_Bor45CII = Brucella ovis ATCC 25840 chromosome II (NC_009504), αr45_Bmir45CII = Brucella microti CCM 4915 chromosome 2 (NC_013118), αr45_Oar45C = Ochrobactrum anthropi ATCC 49188 chromosome 2 (NC_009668), αr45_MsBNCr45C = Mesorhizobium sp. BNC1 (NC_008254), αr45_Bahr45C = Bartonella henselae str. Houston-1 (NC_005956), αr45_Bacr45C = Bartonella clarridgeiae 73 (NC_014932), αr45_Batr45C = Bartonella tribocorum CIP 105476 (NC_010161), αr45_Baqr45C = Bartonella quintana str. Toulouse (NC_005955), αr45_Babr45C = Bartonella bacilliformis KC583 (NC_008783), αr45_Bagr45C = Bartonella grahamii as4aup (NC_012846), αr45_Ac571r45C = Azorhizobium caulinodans ORS 571 (NC_009937), αr45_Stnr45C = Starkeya novella DSM 506 chromosome (NC_014217), αr45_Xar45C = Xanthobacter autotrophicus Py2 chromosome (NC_009720), αr45_Mesr45C = Methylocella silvestris BL2 chromosome (NC_011666), αr45_Beir45C = Beijerinckia indica subsp. indica ATCC 9039 chromosome (NC_010581), αr45_Rhpr45C = Rhodopseudomonas palustris BisA53 chromosome (NC_008435).
English: Sinorhizobium meliloti 45 family
Außenwinkelhablierenden (rot gestrichelt):
Die 3 Schnittpunkte D, E, F liegen auf einer Geraden (rot) und es gelten die folgenden Streckenverhältnisse:
 
  
    
      
        
          
            
              
                
                  |
                
                E
                B
                
                  |
                
              
              
                
                  |
                
                E
                C
                
                  |
                
              
            
          
        
        =
        
          
            
              
                
                  |
                
                A
                B
                
                  |
                
              
              
                
                  |
                
                A
                C
                
                  |
                
              
            
          
        
      
    
    {\displaystyle {\tfrac {|EB|}{|EC|}}={\tfrac {|AB|}{|AC|}}}
  
, 
  
    
      
        
          
            
              
                
                  |
                
                F
                B
                
                  |
                
              
              
                
                  |
                
                F
                A
                
                  |
                
              
            
          
        
        =
        
          
            
              
                
                  |
                
                C
                B
                
                  |
                
              
              
                
                  |
                
                C
                A
                
                  |
                
              
            
          
        
      
    
    {\displaystyle {\tfrac {|FB|}{|FA|}}={\tfrac {|CB|}{|CA|}}}
  
, 
  
    
      
        
          
            
              
                
                  |
                
                D
                A
                
                  |
                
              
              
                
                  |
                
                D
                C
                
                  |
                
              
            
          
        
        =
        
          
            
              
                
                  |
                
                B
                A
                
                  |
                
              
              
                
                  |
                
                B
                C
                
                  |
                
              
            
          
        
      
    
    {\displaystyle {\tfrac {|DA|}{|DC|}}={\tfrac {|BA|}{|BC|}}}
Короны с шестью, восемью и десятью вершинами

вершин = 2 n

рёбер = n (n — 1)

хроматическое число = 
  
    
      
        
          {
          
            
              
                
                  1
                
                
                  n
                  =
                  1
                
              
              
                
                  2
                
                
                  
                    otherwise
                  
                
              
            
          
          
        
      
    
    {\displaystyle \left\{{\begin{array}{ll}1&n=1\\2&{\text{otherwise}}\end{array}}\right.}
  


радиус = 
  
    
      
        
          {
          
            
              
                
                  ∞
                
                
                  n
                  ≤
                  2
                
              
              
                
                  3
                
                
                  
                    otherwise
                  
                
              
            
          
          
        
      
    
    {\displaystyle \left\{{\begin{array}{ll}\infty &n\leq 2\\3&{\text{otherwise}}\end{array}}\right.}
  


диаметр = 
  
    
      
        
          {
          
            
              
                
                  ∞
                
                
                  n
                  ≤
                  2
                
              
              
                
                  3
                
                
                  
                    otherwise
                  
                
              
            
          
          
        
      
    
    {\displaystyle \left\{{\begin{array}{ll}\infty &n\leq 2\\3&{\text{otherwise}}\end{array}}\right.}
  


обхват = 
  
    
      
        
          {
          
            
              
                
                  ∞
                
                
                  n
                  ≤
                  2
                
              
              
                
                  6
                
                
                  n
                  =
                  3
                
              
              
                
                  4
                
                
                  
                    otherwise
                  
                
              
            
          
          
        
      
    
    {\displaystyle \left\{{\begin{array}{ll}\infty &n\leq 2\\6&n=3\\4&{\text{otherwise}}\end{array}}\right.}
  


свойства = дистанционно-транзитивный

обозначение = 
  
    
      
        
          S
          
            n
          
          
            0
          
        
      
    
    {\displaystyle S_{n}^{0}}
Decriminalization of same-sex sexual activity by country or territory    1790–1799   1800–1829   1830–1839   1840–1859   1860–1869   1870–1879   1880–1889   1890–1929   1930–1939   1940–19491   1950–1959   1960–1969   1970–1979   1980–1989   1990–19992   2000–2009   2010–present   Same-sex sexual activity legal3   Male same-sex sexual activity illegal   Same-sex sexual activity illegal  Notes  1: During World War II, Nazi Germany annexed territory or established reichskommissariats which extended Germany's laws against same-sex sexual activity to those territories and reichskommissariats. Same-sex sexual activity was previously legalized in the following countries or territories before German annexation or establishment of reichskommissariats: Bas-Rhin (legal in 1791), Belgium (legal in 1795), Belluno (legal in 1890), Friuli-Venezia Giulia (legal in 1890), Haut-Rhin (legal in 1791), Luxembourg (legal in 1795), Moselle (legal in 1791), Netherlands (legal in 1811), Nord (legal in 1791), Pas-de-Calais (legal in 1791), Poland (legal in 1932), and Trentino-Alto Adige / Südtirol (legal in 1890). All countries and territories listed that where annexed or established into reichskommissariats by Nazi Germany during World War II where restored as independent countries or reincorporated into their previous countries during or after the war and thus re-legalized same-sex sexual activity in those areas.
 2: In May 1973, the Libyan Arab Republic annexed the Aouzou Strip from Chad. Libya's laws against same-sex sexual activity where thus extended to the annexed Aouzou Strip. In August 1987, during the Toyota War between the Great Socialist People's Libyan Arab Jamahiriya and Chad, Aouzou fell to the Chadian forces, only to be repelled by an overwhelming Libyan counter-offensive. The Aouzou dispute was concluded on 3 February 1994, when the judges of the International Court of Justice by a majority of 16 to 1 decided that the Aouzou Strip belonged to Chad. Monitored by international observers, the withdrawal of Libyan troops from the Strip began on 15 April 1994, and was completed by 10 May 1994. The formal and final transfer of the Aouzou Strip from Libya to Chad took place on 30 May 1994, when the sides signed a joint declaration stating that the Libyan withdrawal had been effected.
 3: Same-sex sexual activity was never criminalized in the following countries and territories: Benin, Burkina Faso, Cambodia Central African Republic, Chad (excluding Aouzou Strip), Clipperton Island, Republic of the Congo, Côte d'Ivoire, Democratic Republic of Congo, French Polynesia, French Southern and Antarctic Lands, Gabon, Laos, Madagascar, Mali, Mayotte, New Caledonia, Niger, North Korea, Rwanda, South Korea, Vietnam, and Wallis and Futuna. Same-sex sexual activity had also never been criminalized in continent of Antarctica.
Figur 4: De eulerska trianglarna 
  
    
      
        △
        A
        
          B
          
            1
          
        
        C
      
    
    {\displaystyle \triangle AB_{1}C}
  
 och 
  
    
      
        △
        A
        
          B
          
            2
          
        
        C
      
    
    {\displaystyle \triangle AB_{2}C}
  
 har sidan 
  
    
      
        b
      
    
    {\displaystyle b}
  
 och vinklarna 
  
    
      
        α
      
    
    {\displaystyle \alpha }
  
 och 
  
    
      
        β
      
    
    {\displaystyle \beta }
  
 lika. Vinklarna 
  
    
      
        β
      
    
    {\displaystyle \beta }
  
 är lika eftersom båda storcirklarna till 
  
    
      
        
          a
          
            1
          
        
      
    
    {\displaystyle a_{1}}
  
 respektive 
  
    
      
        
          a
          
            2
          
        
      
    
    {\displaystyle a_{2}}
  
 tangerar den orange parallellcirkeln med radien 
  
    
      
        
          
            
              π
              2
            
          
          −
          β
        
      
    
    {\displaystyle \textstyle {\frac {\pi }{2}}-\beta }
  
 till storcirkeln 
  
    
      
        
          
            
              A
              
                B
                
                  1
                
              
              
                B
                
                  2
                
              
            
            ¯
          
        
      
    
    {\displaystyle {\overline {AB_{1}B_{2}}}}
  
, på varsin sida om och lika långt från meridianen genom 
  
    
      
        C
      
    
    {\displaystyle C}
  
. Sålunda är 
  
    
      
        
          a
          
            1
          
        
        +
        
          a
          
            2
          
        
        =
        π
      
    
    {\displaystyle a_{1}+a_{2}=\pi }
  
 och 
  
    
      
        sin
        ⁡
        
          a
          
            1
          
        
        =
        sin
        ⁡
        
          a
          
            2
          
        
      
    
    {\displaystyle \sin a_{1}=\sin a_{2}}
  
. Denna typ av obestämdhet förekommer inte hos plana trianglar, eftersom vinkelsumman i sådana alltid är 
  
    
      
        π
      
    
    {\displaystyle \pi }
  
: eftersom 
  
    
      
        α
      
    
    {\displaystyle \alpha }
  
 och 
  
    
      
        β
      
    
    {\displaystyle \beta }
  
 är givna, är även vinkeln i 
  
    
      
        C
      
    
    {\displaystyle C}
  
 (
  
    
      
        =
        π
        −
        α
        −
        β
      
    
    {\displaystyle =\pi -\alpha -\beta }
  
) given.
Stjepan Tomašević Kotromanić (oko 1438 — 5. juni 1463.) je bio vladar iz dinastije Kotromanić, koji je bio poslednji despot Srbije (21. mart 1459 — 20. juni 1459.) i kralj Srba, Bosne, Primorja, Humske zemlje, Donjih Kraja, Usore, Soli, Podrinja i Zapadnih strana[1] (10. juli 1461 - 5. juni 1463). Tokom svoje kratkotrajne vladavine je pred nadmoćnom osmanskom vojskom bez borbe predao Smederevo i Srpsku despotovinu, a potom i Kraljevinu Bosnu posle opsade Ključa. Predao se Mahmud paši Anđeloviću uz obećanje da će mu biti pošteđen život, ali je bio izveden pred sultana Mehmeda II (1451 — 1481) u Jajcu i tu je na licu mesta pogubljen po njegovoj naredbi.Stjepan Tomašević došao je na vlast nakon očeve smrti 1461. godine. Svjestan opasnosti koja mu je prijetila, Tomašević je već 1461. godine u poslanici papi Piu II predvidio tursku najezdu velikih razmjera i zamolio ga za pomoć Bosni.Sljedeće godine priznao je vrhovnu vlast hrvatsko-ugarskog kralja Matije I Ugarskog i očekujući pomoć iz Hrvatske i Ugarske, otkazao sultanu plaćanje danka. Na početku 1463. godine obratio se opet Mlecima upozoravajući ih da Turci smjeraju tog ljeta zauzeti svu Bosnu , a da će nakon toga zaprijetiti i mletačkim posjedima u Dalmaciji. Ali pomoći niotkuda.Velika turska vojska pod vodstvom Mehmeda II Osvajača okupila se u proljeće 1463. godine u Drinopolju i krenula na Bosnu. Prva bosanska tvrđava koja je pala (20. maja) bijaše stari kraljevski tvrdi grad Bobovac. Kralj Stjepan Tomašević izbjegao je na sjever, u Jajce, i sklonio se u obližnju tvrđavu Ključ . Opkoljen Turcima, predao se, uz tursko obećanje da će mu poštedjeli život. Međutim, odveden je u Jajce, zajedno sa amidžom Radivojem, gdje su obojica pogubljeni. Poslije su nastale priče o tome kako je izdan i zatim smaknut. Ali slučajno imamo iskaz svjedoka o tome u uspomenama turskog janjičara srpskog porijekla, od čijeg se stvarnosnog opisa ledi krv u žilama: "Kad su kraljeve sluge koje su bile u tvrđavi vidjele da im je gospodar zarobljen, predale su se. Sultan je zauzeo tvrđavu i zapovjedio da se kralj i njegovi sudnizi pogube. I zatim je zauzeo svu njegovu zemlju." Iza Stjepana Tomaševića ostala je njegova udovica, tada šesnaestogodišnja kraljica Marija, kći despota Lazara Brankovića, te njihovo dvoje, u izvorima neiomenovane, djece.Udovica Stjepana Tomaša, kraljica Katarina Kosača, uspjela je preko Kupresa i Dubrovnika pobjeći u Rim , gdje je i umrla 1478. godine, a grobnica joj se još može vidjeti u crkvi Santa Maria in Aracoeli na Kapitolu. Dvoje njihove djece, Sigismund , poslije smrti Stjepana nasljednik bosanske krune, i mala Katarina Bosanska je zarobljena i odvedena u Istanbul. Tako se ugasila loza Kotromanića. Posmrtni ostaci kralja Stjepana Tomaševića pohranjeni su unutar franjevačkog samostana u Jajcu.
Portraits of Kings of France is a serie of portraits commissioned between 1837 and 1838 by Louis Philippe I and painted by various artists for the Musée historique de Versailles.
Nikel(II)-aren konplexuen kolore ezberdinak ur disoluzioan, ezkerretik hasita: 
  
    
      
        
          
            
              [
              Ni
              
                
                  (
                  
                    NH
                    
                      3
                    
                    
                      
                    
                  
                  )
                
                
                  6
                
                
                  
                
              
              ]
            
            
              2
              
              +
            
          
          ,
          
            
              [
              Ni
              
                (
                
                  C
                  
                    2
                  
                  
                    
                  
                
                
                  H
                  
                    4
                  
                  
                    
                  
                
                
                  
                    (
                    
                      NH
                      
                        2
                      
                      
                        
                      
                    
                    )
                  
                  
                    2
                  
                  
                    
                  
                
                )
              
              ]
            
            
              2
              
              +
            
          
          ,
          
            
              [
              
                NiCl
                
                  4
                
                
                  
                
              
              ]
            
            
              2
              
              
                −
              
            
          
          ,
          
            
              [
              Ni
              
                
                  (
                  
                    H
                    
                      2
                    
                    
                      
                    
                  
                  O
                  )
                
                
                  6
                
                
                  
                
              
              ]
            
            
              2
              
              +
            
          
        
      
    
    {\displaystyle {\ce {[Ni(NH3)6]^{2+}, [Ni(C2H4(NH2)2)]^{2+}, [NiCl4]^{2-}, [Ni(H2O)6]^{2+}}}}
English: Color of various Ni(II) complexes in aqueous solution. From left to right, hexaamminenickel(II), tris(ethylenediamine)nickel(II), tetrachloronickelate(II) and hexaaquanickel(II)