항목

  • Hamming code
    With \vec{a} = a_1 a_2 a_3 a_4 with a_i exist in F_2 (A field with two elements namely 0 and 1).Thus the codewords are all the 4-tuples (k-tuples).Therefore,(1,0,1,1) gets encoded as (1,0,1,1,0,1,0). The [7,4] Hamming code can easily be extended to an [8,4] code by adding an extra parity bit on...
  • Rotatum
    d \vec \tau}{dt} where τ is torque and \frac{\mathrm{d}}{\mathrm{d}t} is the derivative with respect to time t.The term rotatum is not universally recognized but is commonly used. this word derived from Latin word rotātus meaning to rotate. The units of rotatum are force times distance per time...
  • Big O notation
    n^2 + m^3 + g(n,m).\, Note that this definition allows all of the coordinates of \vec{x} to increase to infinity. In particular, the statement f(n,m) = O(n^m) \text{ as } n,m\to\infty\, (i.e., \exists C\,\exists M\,\forall n\,\forall m\dots) is quite different from \forall m\colon f(n,m) = O(n^m...
  • Fibonacci number 피보나치 수, フィボナッチ数
    n}\vec\nu~\\ & =\cfrac{1}{\sqrt{5}}\cdot\left(\cfrac{1+\sqrt{5}}{2}\right)^n{\varphi \choose 1}-\cfrac{1}{\sqrt{5}}\cdot\left(\cfrac{1-\sqrt{5}}{2}\right)^n{-\varphi^{-1}\choose 1}~, \end{align} from which the th element in the Fibonacci series as an analytic function of is now read off directly...
  • Mathematics of general relativity 一般相対論の数学, 廣義相對論..
    ds^2 = g_{ab} \, dx^a \, dx^b This way of expressing the metric was used by the pioneers of differential geometry. While some relativists consider the notation to be somewhat old-fashioned, many readily switch between this and the alternative notation: g = g_{ab} \, dx^a \otimes dx^b The metric...
  • Quantum-mechanical explanation of intermolecular interactions
    The word symmetry refers here to permutational symmetry of electrons). The different approaches shared a major drawback: they were very difficult to apply in practice. Hence a somewhat less rigorous approach (weak symmetry forcing) was introduced: apply ordinary RS-PT and introduce the...
  • Magnetohydrodynamics
    the word magnetohydrodynamics is by Hannes Alfvén in 1942: "At last some remarks are made about the transfer of momentum from the Sun to the planets, which is fundamental to the theory (§11). The importance of the magnetohydrodynamic waves in this respect are pointed out." The ebbing salty...
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