By Ross Kindermann
The examine of Markov random fields has introduced interesting new difficulties to likelihood conception that are being built in parallel with uncomplicated research in different disciplines, such a lot significantly physics. The mathematical and actual literature is usually particularly technical. This ebook goals at a extra mild advent to those new components of study.
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D* + u] = - lA2n+2^ n+ iD (Z)2)-i, D* + u}+0 (Dr or The remaining terms must vanish, because the commutator of two differential operators can only be a differential operator. Thus, the (2n + l)-th order operator Q has the required property - its commutator with D2 + u is the operator of multiplication by a function, [Q D2 + u] = 2iA' LV ' ' J 2n-f2,n+± i = 4i 4~ #n+i Mcte n+11 J As might be expected, the commutator is the right-hand side of the Korteweg—de Vries equation. References [1 ] I. M.