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Ludwig II was King of Bavaria from 1864 until his death in 1886. He is sometimes called the Swan King or der Märchenkönig ("the Fairy Tale King").
In mathematical physics, more specifically the one-dimensional inverse scattering problem, the Marchenko equation , named after Israel Gelfand, Boris Levitan and Vladimir Marchenko, is derived by computing the Fourier transform of the scattering relation: K ( r , r ′ ) + g ( r , r ′ ) + ∫ r ∞ K ( r , r ′ ′ ) g ( r ′ ′ , r ′ ) d r ′ ′ = 0 {\displaystyle K(r,r^{\prime })+g(r,r^{\prime })+\int _{r}^{\infty }K(r,r^{\prime \prime })g(r^{\prime \prime },r^{\prime })\mathrm {d} r^{\prime \prime }=0} Where g ( r , r ′ ) {\displaystyle g(r,r^{\prime })\,} is a symmetric kernel, such that g ( r , r ′ ) = g ( r ′ , r ) , {\displaystyle g(r,r^{\prime })=g(r^{\prime },r),\,} which is computed from the scattering data. Solving the Marchenko equation, one obtains the kernel of the transformation operator K ( r , r ′ ) {\displaystyle K(r,r^{\prime })} from which the potential can be read off.
Marchenko and Martchenko is a Ukrainian surname of the following people:
Marchenoir is a commune in the Loir-et-Cher department of central France. The nearby forest of Marchenoir was the site of L'Aumône Abbey, a Cistercian daughter house of Cîteaux Abbey.
In the mathematical theory of random matrices, the Marchenko–Pastur distribution, or Marchenko–Pastur law, describes the asymptotic behavior of singular values of large rectangular random matrices. The theorem is named after Ukrainian mathematicians Vladimir Marchenko and Leonid Pastur who proved this result in 1967.