fschieber/wit-captions huggingface dataset:
Beispiel: 
  
    
      
        
          V
          
            i
          
        
      
    
    {\displaystyle V_{i}}
  
 ist gleichverteilt über 
  
    
      
        [
        0
        ,
        10
        ]
      
    
    {\displaystyle [0,10]}
  
; 
  
    
      
        
          v
          
            0
          
        
        =
        0
      
    
    {\displaystyle v_{0}=0}
  
 (blaue Kurve) bzw. 
  
    
      
        
          v
          
            0
          
        
        =
        2
      
    
    {\displaystyle v_{0}=2}
  
 (rote Kurve). Bei 
  
    
      
        
          v
          
            0
          
        
        =
        0
      
    
    {\displaystyle v_{0}=0}
  
 kann mit einem Mindestpreis von 
  
    
      
        
          r
          
            ∗
          
        
        =
        5
      
    
    {\displaystyle r^{*}=5}
  
 der maximale erwartete Erlös erzielt werden. Der ex ante erlösoptimierende Mindestpreis 
  
    
      
        
          r
          
            ∗
          
        
      
    
    {\displaystyle r^{*}}
  
 steigt in 
  
    
      
        
          v
          
            0
          
        
      
    
    {\displaystyle v_{0}}
  
; mit 
  
    
      
        
          v
          
            0
          
        
        =
        2
      
    
    {\displaystyle v_{0}=2}
  
 beträgt er hier etwa bereits 
  
    
      
        
          r
          
            ∗
          
        
        =
        6
      
    
    {\displaystyle r^{*}=6}
  
. (Quelltext/Berechnung)
Figure 4. A four-wave mixing process in which two photons with 
  
    
      
        
          k
          
            x
          
        
        =
        
          k
          
            y
          
        
        =
        0
      
    
    {\displaystyle k_{x}=k_{y}=0}
  
 are absorbed and two photons with 
  
    
      
        
          k
          
            x
          
        
        =
        
          
            
              
                k
                ¯
              
            
          
          
            x
          
        
        ,
        
          k
          
            y
          
        
        =
        0
      
    
    {\displaystyle k_{x}={\bar {k}}_{x},k_{y}=0}
  
 and 
  
    
      
        
          k
          
            x
          
        
        =
        −
        
          
            
              
                k
                ¯
              
            
          
          
            x
          
        
        ,
        
          k
          
            y
          
        
        =
        0
      
    
    {\displaystyle k_{x}=-{\bar {k}}_{x},k_{y}=0}
  
 are emitted. 
  
    
      
        
          k
          
            x
          
        
      
    
    {\displaystyle k_{x}}
  
, 
  
    
      
        
          k
          
            y
          
        
      
    
    {\displaystyle k_{y}}
  
 and 
  
    
      
        
          k
          
            z
          
        
      
    
    {\displaystyle k_{z}}
  
 are the components of the wave-vectors.
English: four wave mixing process
Zusammensetzung der neu gewählten Lok Sabha (Farbgebung wie oben), Kleinparteien ohne Farbe sind von der Sitzordnung den Parteien zugeordnet, die sie unterstützen. Zwei Abgeordnete werden durch den Staatspräsidenten ernannt.  1. UPA: 221
﻿Indischer Nationalkongress 145
 ﻿Nationalist Congress Party 9
 ﻿Dravida Munnetra Kazhagam 16
 ﻿Rashtriya Janata Dal 24
 ﻿Pattali Makkal Katchi 6
 ﻿Telangana Rashtra Samithi 5
 ﻿Lok Janshakti Party 4
 ﻿Marumalarchi Dravida Munnetra Kazhagam 4
 ﻿Jammu and Kashmir People’s Democratic Party 1
 ﻿Jharkhand Mukti Morcha 5
 ﻿Andere UPA-Parteien: 2
       Indian Union Muslim League 1,
       Republican Party of India (A.) 1
 2. NDA: 181
 ﻿BJP 138
 ﻿Shiv Sena 12
 ﻿Shiromani Akali Dal 8
 ﻿Janata Dal (United) 8
 ﻿Nationalist Trinamool Congress 2
 ﻿Biju Janata Dal 11
 ﻿Andere NDA-Parteien: 2:
       Nagaland People’s Front 1,
       Mizo Democratic Front 1
 3. Alle übrigen: 82
 ﻿Samajwadi Party 36
 ﻿Bahujan Samay Party 19
 ﻿Telugu Desam Party 5
 ﻿Rashtriya Lok Dal 3
 ﻿Janata Dal (Secular) 3
 ﻿Jammu & Kashmir National Conference 2
 ﻿Asom Gana Parishad 2
 ﻿Andere und Unabhängige 12:
       AI Majlis-e-Ittehadul Muslimeen 1
       Kerala Congress 1
       Sikkim Democratic Front 1
       National Loktantrik Party 1
       Samajwadi Janata Party (R.) 1
       Indian Federal Democratic Party 1
       Bharatiya Navshakti Party 1
       Unabhängige 5  4. Kommunistische und linkssozialistische Parteien: 59
 ﻿CPI (Marxist) 43
 ﻿Kommunistische Partei Indiens 10
 ﻿Revolutionary Socialist Party 3
 ﻿All India Forward Bloc 3
 5. Nominierte: 2
 ﻿vom Staatspräsidenten ernannt 2
單位向量 
  
    
      
        
          
            
              
                
                  e
                
                
                  i
                
              
              ^
            
          
        
      
    
    {\displaystyle {\hat {\mathbf {e} _{i}}}}
  
 與參考系的三個單位向量 
  
    
      
        
          
            
              
                
                  x
                
                ^
              
            
          
          
            1
          
        
      
    
    {\displaystyle {\hat {\mathbf {x} }}_{1}}
  
 、
  
    
      
        
          
            
              
                
                  x
                
                ^
              
            
          
          
            2
          
        
      
    
    {\displaystyle {\hat {\mathbf {x} }}_{2}}
  
 、
  
    
      
        
          
            
              
                
                  x
                
                ^
              
            
          
          
            3
          
        
      
    
    {\displaystyle {\hat {\mathbf {x} }}_{3}}
  
 之間的夾角分別為 
  
    
      
        
          θ
          
            i
            1
          
        
      
    
    {\displaystyle \theta _{i1}}
  
 、
  
    
      
        
          θ
          
            i
            2
          
        
      
    
    {\displaystyle \theta _{i2}}
  
 、
  
    
      
        
          θ
          
            i
            3
          
        
      
    
    {\displaystyle \theta _{i3}}
  
 。
Stan cząstki w pudle potencjału obliczony z zasad dynamiki Newtona (mechanika klasyczna) przedstawiający cykliczny ruch między ścianami pudła (A) oraz stan układu kwantowego obliczony z równania Schrödingera (mechanika kwantowa) (B-F). W przypadkach (B-F), pozioma oś oznacza położenie, pionowa natomiast rzeczywistą (kolor niebieski) i urojoną (kolor czerwony) część funkcji falowej. Stany (B,C,D) są stanami własnymi hamiltonianu 
  
    
      
        
          ψ
          
            1
          
        
        ,
        
          ψ
          
            2
          
        
        ,
        
          ψ
          
            3
          
        
      
    
    {\displaystyle \psi _{1},\psi _{2},\psi _{3}}
  
 o ściśle określonych energiach. Stany (E,F) są superpozycjami stanów własnych hamiltonianu, dlatego nie mają ściśle określonej energii. Jednak średnia energia tych stanów jest stała w czasie.Prawdopodobieństwa znalezienia cząstki dla stanów własnych 
  
    
      
        P
        (
        x
        ,
        t
        )
        =
        
          |
        
        
          ψ
          
            n
          
        
        (
        x
        ,
        t
        )
        
          
            |
          
          
            2
          
        
        ,
        n
        =
        1
        ,
        2
        ,
        3
      
    
    {\displaystyle P(x,t)=|\psi _{n}(x,t)|^{2},n=1,2,3}
  
 zależą tylko od położenia, a nie zależą od czasu. Dla stanów (E,F) prawdopodobieństwa te zmieniają się w czasie, analogicznie jak dla cząstki klasycznej.
English: Trajectories of a particle in a box (also called an infinite square well) in classical mechanics (A) and quantum mechanics (B-F). In (A), the particle moves at constant velocity, bouncing back and forth. In (B-F), wavefunction solutions to the Time-Dependent Schrodinger Equation are shown for the same geometry and potential. The horizontal axis is position, the vertical axis is the real part (blue) or imaginary part (red) of the wavefunction. (B,C,D) are stationary states (energy eigenstates), which come from solutions to the Time-Independent Schrodinger Equation. (E,F) are non-stationary states, solutions to the Time-Dependent but not Time-Independent Schrodinger Equation. Both (E) and (F) are randomly-generated superpositions of the four lowest-energy eigenstates, (B-D) plus a fourth not shown.
The square acbd represents an instanton, i.e, the family of trajectories of deterministic flow (dotted arrowed curves) leading from one critical point (b) to another (a). The bra/ket (
  
    
      
        ⟨
        a
        
          |
        
      
    
    {\displaystyle \langle a|}
  
/
  
    
      
        
          |
        
        b
        ⟩
      
    
    {\displaystyle |b\rangle }
  
) of the locally supersymmetric ground states (vacua) corresponding to these critical points are the Poincare duals of the local unstable/stable manifolds. Operators 
  
    
      
        
          
            
              
                O
                ^
              
            
          
          
            1
            ,
            2
          
        
      
    
    {\displaystyle {\hat {O}}_{1,2}}
  
 are Poincare duals of vertical/horizontal lines. The value of the instantonic matrix element is the intersection number (the difference in the numbers of positive (black) and negative (white) intersections). It is invariant under the temporal evolution due to the flow, 
  
    
      
        
          
            
              
                O
                ^
              
            
          
          
            1
          
        
        (
        0
        )
        →
        
          
            
              
                O
                ^
              
            
          
          
            1
          
        
        (
        t
        )
      
    
    {\displaystyle {\hat {O}}_{1}(0)\to {\hat {O}}_{1}(t)}
  
 .
English: Figure representing instanton matrix element in STS
Logical computations, i.e. tasks, partially define phenotypes, and phenotypic matching leads to ecological interactions Digital organisms process binary numbers taken from the environment using the instructions that constitute their genomes. When the output of processing those numbers equals the result of applying a logic function, the digital organism is said to have performed that task. The combination of tasks performed by a digital organism partially defines its phenotype. The center of the figure depicts the output of applying eight logical operators (tasks) on the two input numbers above. On the left and right, five hypothetical host (green) and parasite (red) phenotypes are represented as columns (on the top) and as circles (below). On the top, each column depicts a phenotype and each row represents a task. Tasks performed by each phenotype are filled. In the lower part, the interaction networks between hosts and parasites are illustrated, which result from phenotypic matching: a parasite infects a host (indicated by a line) if it performs at least one task that is also performed by the host. Inset numbers indicate the identity of phenotypes represented on the top. Arrows represent the temporal direction of the coevolutionary process: from the earliest phenotype to the most recent one. The order of tasks (from top to bottom) indicates the time needed for a digital organism to perform that task over the course of the evolutionary trajectory. Depending on the pattern of tasks performed by the digital organisms, a modular (left) or nested (right) interaction network can emerge.
ජාතික ගීය Soldier’s Song අගනුවර (හා විශාලම නගරය) ඩබ්ලින් (Dublin) භාෂාව අයිරිෂ්, ඉංග්‍රීසි ජාතීන් 90% අයර්ලන්ත, 7.5% වෙනත් යුරෝපීය ජාතීන්, 1.3% ආසියානු, 1.1% කළු ජා‍තියේ නාමය අයර්ලන්ත (Irish) රජය ප්‍රජාතාන්ත්‍රික, ව්‍යවස්ථික ජනරජයක්, පාර්ලිමේන්තු ක්‍රමය ක්‍රියාත්මක වේ. ජනපති Mory McAleesha ආණ්ඩුකරු Brion Cowen, TD (Tonseach - රජය භාරවන්නේ මොහුටයි) උප අගමැති Mors Caughlan, TD (Tonsle) (TD – Teachte Dele –එනම් ව්‍යවස්ථා සම්පාදනය කරන මඩුල්ලේ Dail Eireonn ආයතන නියෝජිතයන්ය) ව්‍යවස්ථා සම්පාදනය යනු සාමාජිකයන් 226 කින් සමන්විත මඩුල්ලකි. මෙහි 60 ක් සෙනෙට් සභාව වේ. නිදහස            මහා බ්‍රිතාන්‍යයෙන් ප්‍රකාශ කිරීම	-	1916 අප්‍රේල් 24 වලංගු වීම	-	1919 ජනවාරි 21 නිදහස් රාජ්‍යයක් ලෙස පිළි ගැනීම - 1937 දෙසැම්බර් 6 වර්තමාන ව්‍යවස්ථාව පිහිටුවීම - 1937 දෙසැම්බර් 29  භූමි ප්‍රමාණය වර්ග කි. මී. 70 273 වර්ග සැතපුම් 27 133 ජල ප්‍රතිශතය 2% යුරෝපීය සංවිධානය (Eu) සාමාජිකත්වය 1973 ජනවාරි 1 සිට ජනගහනය 2009 දී 4, 460, 000 වන බවට ඇස්තමේන්තු කර ඇත. 2006 සංගණනයට අනුව 4, 239, 848ලොව ජනගහනය අතරින් 121 වන ස්ථානය ජන ඝනත්වය වර්ග කි. මී. යට 66.3 (67), වර්ග සැතපුමට 147.6 (148), ලොව ඝනත්වය අතරින් 139 වන ස්ථානය දළ දේශීය නිෂ්පාදිතය (ක්‍රය ශක්තිය) ඩොලර් බිලියන 174 (ලොව 54 වන ස්ථානය) 2009 ඒක පුද්ගල - $ 39 441 (ලොව 8 ස්ථානය) දළ ජාතික නිෂ්පාදිතය (නාමික) ඩොලර් බිලියන 226 (ලොව 35 වන ස්ථානය), 2009	 ඒක පුද්ගල $ 51 128 (ලොව 8 වන ස්ථානය) පුද්ගල ප්‍රවර්ධන දර්ශකය (HDI)(2009) 0.965 (ඉතා ඉහල) (ලොව 5 වන ස්ථානය) මුදල් වර්ගය යූරෝ වේලා කලාපය (Time Zone) බටහිර යුරෝපීය වේලාව (UTC + 0) (WET), DSTඅනුව ගිම්හානයේදී (UTC + 1) රථවාහන ධාවනය වම අන්තර්ජාල වසම (Domain) .ie (eg - www.abcd.ie) (TLD – Top Level Domain) දුරකථන කේතය (Country Code) (+353)
English: Irish Flag
Vortex photon (blue) with linear momentum 
  
    
      
        
          P
        
        =
        ℏ
        
          k
        
      
    
    {\displaystyle \mathbf {P} =\hbar \mathbf {k} }
  
 and angular momentum 
  
    
      
        L
        =
        ±
        ℏ
        ℓ
      
    
    {\displaystyle L=\pm \hbar \ell }
  
 are reflected from perfect phase-conjugating mirror. Normal to mirror is 
  
    
      
        
          
            
              n
              →
            
          
        
      
    
    {\displaystyle {\vec {n}}}
  
 , propagation axis is 
  
    
      
        
          
            
              z
              →
            
          
        
      
    
    {\displaystyle {\vec {z}}}
  
. Reflected photon (magenta) has opposite linear momentum 
  
    
      
        
          P
        
        =
        −
        ℏ
        
          k
        
      
    
    {\displaystyle \mathbf {P} =-\hbar \mathbf {k} }
  
 and angular momentum 
  
    
      
        L
        =
        ∓
        ℏ
        ℓ
      
    
    {\displaystyle L=\mp \hbar \ell }
  
. Because of conservation laws PC mirror experiences recoil: the vortex phonon (orange) with doubled  linear momentum 
  
    
      
        
          P
        
        =
        2
        ℏ
        
          k
        
      
    
    {\displaystyle \mathbf {P} =2\hbar \mathbf {k} }
  
 and angular momentum 
  
    
      
        L
        =
        ±
        2
        ℏ
        ℓ
      
    
    {\displaystyle L=\pm 2\hbar \ell }
  
 is excited within mirror.
English: reflection of the vortex photon from phase-conjugating mirror
1. Office and barracks of Hitler's bodyguard
 2. FBK/RSD command post
 3. Emergency generator 
 4. Bunker
 5. Office of Otto Dietrich, Hitler's press secretary 
 6. Conference room, site of the 20 July 1944 assassination attempt
 7. RSD command post 
 8. Guest bunker and air-raid shelter
 9. RSD command post
 10. Secretariat under Philipp Bouhler
 11. Headquarters of Johann Rattenhuber, SS chief of Hitler's security department, and Post Office
 12. Radio and telex buildings
 13. Vehicle garages
    14. Railway siding for Hitler's Train
 15. Cinema
 16. Generator buildings
 17. Quarters of Morell, Bodenschatz, Hewel, Voß, Wolff, and Fegelein
 18. Stores
 19. Residence of Martin Bormann, Hitler's personal secretary
 20. Bormann's personal air-raid shelter for himself and staff
 21. Office of Hitler's adjutant and the Wehrmacht's personnel office
 22. Military and staff mess II
 23. Quarters of General Alfred Jodl, Chief of Operations of OKW
 24. Firefighting pond
 25. Office of the Foreign Ministry
 26. Quarters of Fritz Todt, then Albert Speer after Todt's death 
    27. RSD command post
 28. Air-raid shelter with Flak and MG units on the roof
 29. Hitler's bunker and air-raid shelter
 30. New tea room
 31. Residence of General Field Marshal Wilhelm Keitel, supreme commander of OKW
 32. Old tea house
 33. Residence of Reich Marshal Hermann Göring
 34. Göring's personal air-raid shelter for himself and staff, with Flak and MG on the roof 
 35. Offices of the High Command of the Air Force
 36. Offices of the High command of the Navy
 37. Bunker with Flak 
 38. Ketrzyn railway line
English: map of Wolf's Lair: (Note: This numbering doesn't match the real numbering) 1. Residential premises and Hitler's personal bodyguard 2. Bodyguard and Security Service 3. Emergency generator 4. Bunker 5. Press Chief Dr. Otto Dietrich 6. Conference shack, location of the unsuccessful attack on Hitler of 20 July 1944 7. Security police 8. Air-raid shelter for guests 9. Hitler's personal bodyguards 10. Stenographers 11. Security, first Hitler's bodyguard Rattenhuber, chief of the police department Högl, Post Office 12. Telex 13. Garages 14. Train 15. Cinema 16. Heating buildings 17. Dr. Morell, Bodenschatz, Hewel, Voss, Wolff, Fegelein 18. Commissary 19. Martin Bormann, Hitler's personal secretary 20. Bormann's air-raid shelter 21. Hitler adjutants and Wehrmacht personnel 22. Mess II 23. General Alfred Jodl, Chief of the Operations Staff of the Armed Forces High Command (OKW) 24. Firefighting pond 25. Office of the Foreign Ministry 26. Dr. Fritz Todt, after his fatal accident: Albert Speer 27. Hotel batallion 28. Air-raid shelter with Flak and MG units on the roof 29. Mess I 30. New tearoom 31. General Field Marshal Wilhelm Keitel, chief of the High Command of the Wehrmacht (OKW} 32. Old Teahouse 33. Hermann Göring, Reich Field Marshal, head of the Luftwaffe 34. Göring's air-raid shelter with Flak, MG and reflector units 35. Representation of the High Command of the Air Force 36. Representation of the High Command of the Navy 37. Bunker with Flak Station 38. Railway line Deutsch: Karte der "Wolfsschanze" bei Rastenburg (Kętrzyn) Polski: plan wilczego szańca.
פנקס חסכון של מפעל החסכון באגודות הצרכנים השיתופיות (1958) - מתוך דברי ההסבר על מפעל החסכון: 
 • את הבולים יש לקבל בצרכניה הקבועה שלך. הקפד על תשלומים קבועים! 
 • על חשבון כל יחידת חסכון ישלם החוסך 250 פר' לשבוע בתשלומים קבועים (ארבעה תשלומים לחודש), עד להשלמת הסך 48 ל"י 
 • לכל חוסך יינתן פנקס חסכון. תמורת כל תשלום של 250 פר' יימסר לחוסך בול שיודבק בפנקס החסכון וישמש אשור לסכום ששולם. 
 • סטיפנדיות ותשורות שונות תחולקנה בין החוסכים, לפי גורל, פעמים בשנה 
 • נוסף על הסטיפנדיות ייהנו החוסכים מהשתתפות במפעלים תרבותיים שונים מטעם התנועה הצרכנית. 
 • הקואופרציה הצרכנית הציבה לה מטרה עיקרית אחת – לסייע לחבריה בשיפור תנאי חייהם מבחינה חמרית ורוחנית, לשם קידום ענייניהם הכלכליים והמוסריים גם יחד. 
 • פעולתה של הצרכניה מכוונת לטובת לקוחותיה, כי הם חבריה-בעליה. הצרכניה מקפידה על טיב מעולה של הסחורה, על משקלה הנכון ומחירה הוגן. כל תכליתה לשרת את חבריה. 
 • לשם עבודתה זקוקה הצרכניה לחנות, למדפים, לכלים, להון חוזר, כלומר לכספים שבהם קונים מיצרכים ומשלמים שכר חנות, משכורת לעובדים ויתר ההוצאות. 
 • מפעל החסכון שהתנועה הצרכנית מארגנת יגביר את כוחה של הקואופרציה הצרכנית שתשיג תנאים עוד יותר נוחים – לא לעצמה אלא לחבריה, שהרי כל הצלחתה היא לטובתם. 
 • לחסכונך תתווסף רבית שבחלקה תצורף ליחידתך עם סיום ארבע השנים ולזכותך יהיה סך 50 ל"י במקום 48 שתשלם  
 • כספך שיופקד באגודת הצרכנים שלך יפרה את אגודתך ויאפשר לה להגדיל תועלתך משירותה. 
 • פיתוח הצרכנות השיתופית בישראל מגביר את מעמדו של ציבור העובדים בכפר ובעיר, מבצר את כוחה של המדינה ומסייע לה בקיבוץ גלויות, בפיתוח הארץ, בקליטת העולים ובהשרשתם בענפי המשק היצרניים. 
 • מפעל החסכון חשוב לא לך בלבד. גם חבריך צריכים להצטרף למעגל החוסכים באגודות הצרכנים.
English: Israeli consumers' cooperative's savings notebook (1958)
Regressiongerade 
  
    
      
        
          
            
              y
              ^
            
          
        
      
    
    {\displaystyle {\hat {y}}}
  
 als Schätzer (Modellfunktion) für den Zusammenhang von Größe und Gewicht der Probanden. 
  
    
      
        
          
            
              y
              ^
            
          
        
        (
        
          x
          
            i
          
        
        )
        =
        
          
            
              
                y
                ^
              
            
          
          
            i
          
        
      
    
    {\displaystyle {\hat {y}}(x_{i})={\hat {y}}_{i}}
  
 ist das geschätzte Gewicht des Probanden bei einer gegebenen Größe 
  
    
      
        
          x
          
            i
          
        
      
    
    {\displaystyle x_{i}}
  
. Der Restfehler (das Residuum) 
  
    
      
        
          
            
              
                ε
                ^
              
            
          
          
            i
          
        
      
    
    {\displaystyle {\hat {\varepsilon }}_{i}}
  
 stellt die Differenz zwischen dem Messwert 
  
    
      
        
          y
          
            i
          
        
      
    
    {\displaystyle y_{i}}
  
 und Schätzwert 
  
    
      
        
          
            
              
                y
                ^
              
            
          
          
            i
          
        
      
    
    {\displaystyle {\hat {y}}_{i}}
  
 dar.
The above vector field 
  
    
      
        
          v
        
        =
        
          (
          
            −
            
              
                y
                
                  
                    x
                    
                      2
                    
                  
                  +
                  
                    y
                    
                      2
                    
                  
                
              
            
            ,
            
              
                x
                
                  
                    x
                    
                      2
                    
                  
                  +
                  
                    y
                    
                      2
                    
                  
                
              
            
            ,
            0
          
          )
        
      
    
    {\displaystyle \mathbf {v} =\left(-{\frac {y}{x^{2}+y^{2}}},{\frac {x}{x^{2}+y^{2}}},0\right)}
  
 defined on 
  
    
      
        U
        =
        
          
            R
          
          
            3
          
        
        ∖
        {
        (
        0
        ,
        0
        ,
        z
        )
        ∣
        z
        ∈
        
          R
        
        }
      
    
    {\displaystyle U=\mathbb {R} ^{3}\setminus \{(0,0,z)\mid z\in \mathbb {R} \}}
  
 has zero curl almost everywhere and is thus irrotational. However, it is neither conservative nor does it have path independence.