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चार महीने का बच्चा कैसे बना अरब़पति

चार महीने का बच्चा कैसे बना अरब़पति? जन्म के सिर्फ चार माह बाद यदि कोई बच्चा अरबपति बन जाए तो इसे उसकी किस्मत ही कहेंगे। भारत के एकाग्रह रोहन मूर्ति नाम के बच्चे की किस्मत कुछ इसी प्रकार चमकी है। देश की दूसरी सबसे बड़ी आइटी कम्पनी इंफोसिस के फाउंडर नारायण मूर्ति ने सोमवार अपने चार महीने के पोते एकाग्रह मूर्ति को 240 करोड़ रूपए के शेयरों की हिस्सेदारी का तोहफा देकर उसे शायद देश का सबसे कम उम्र का अरबपति बना दिया है। BSE की फाइलिंग के अनुसार इंफोसिस में अब एकाग्रह रोहन की 15 लाख शेयरों की हिस्सेदारी हो गई है। इसका मतलब अब एकाग्रह रोहन इंफोसिस का 0.04% का हिस्सेदार है। शेयरों के स्थानान्तरण के बाद नारायण मूर्ति के पास कम्पनी के कुल शेयरों का 0.36% हिस्सा बचा है। जिस समय नारायण मूर्ति द्वारा अपने पोते को शेयर देने की खबर बाई उस समय इंफोसिस के शेयरों में गिरावट देखने को मिल रही थी। एकाग्रह रोहन, नारायण मूर्ति तथा सुधा मूर्ति के बेट रोहन मूर्ति और उनकी पत्नि अर्पणा कृष्णन का बेटा है। आपको यह पता होगा कि नोरायण मूर्ति ने अपनी पत्नि सुधा मूर्ति से 10 हजार रूपए उधार लेकर 1981 में इंफोसिस क
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Poisson brackets | Identities of Poisson brackets | Classical Mechanics

Poisson brackets and its identities

Poisson brackets

  • A Poisson bracket is a special kind of relation between a pair of dynamical variables of any holonomic system, which is found to remain invariant under any canonical transformation.
  • They are used to construct new integrals of motion from the known integrals.
  • They are classical analogues of commutation relation between operators in quantum mechanics.
  • If u (p, q, t) and v (p, q, t) are two dynamical variables, then the Poisson bracket of these quantities with respect to canonical variables (p, q) is
                

Identities of Poisson brackets

  • [u, v] = – [v, u]


  • Thus the Poisson bracket of any two dynamical variables is anti-commutative.
  • If u = v, then
                
  • [u, u](p, q) = 0
  • [u, u] = [v, v] = 0

  • If c is any constant, then [cu, v] = [u, cv] = c [u, v]

  • Similarly [u, cv] = c [u, v]
  • ∴  [cu, v] = [u, cv] = c [u, v]

  • The Poisson brackets satisfy the distributive property
  • [u + v, w] = [u, w] + [v, w] and [u, v w] = [u, v]w + v[u, w]

  • Similarly [u, v w] = [u, v]w + v[u, w]

  • The partial derivative of Poisson bracket is

  • Jacobi identity of Poisson bracket is [u [v, w]] + [v [w, u]] + [w [u, v]] = 0

  • If F (w1, w2, …, wn) be a differentiable function of w1, w2, …, wn and all w’s be the function of (p, q, t), then

  • Let F (w1, w2) be a differentiable function of w1 and w2

To know about Poisson bracket and its identities please click on the link for English and  click on the link for Hindi
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