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13 Dec 2018: As an illustration of the method, Figure 1 shows comparisons between the firstand second iterations of the operator series with ’exact’ computations from (24 ),restricted to the rough portion of the ... αr r′. = f(r,r′) (24). the expression (23)

13 Dec 2018: 0 Zl ( (•(x,zi))=--• Do(X)-- likzi cos 0 --• COS 2 0 eikXx+ h(x)• ,. (24). where • is the variance of the surface height. Here we have neglected an O(a ... 29) Collecting terms, and using (25), (26), and (29), Eq. (24) can now be written. ( {•

3 Apr 2018: h7), (2.23). Magnus–Lanczos methods with simplified commutators 15. where. ϕ1(h,ζ,ξ) = h2 4hξ 2ζξ, (2.24).

16 Nov 2018: Doyle and C. McMullen [24]: “But can be solved in the case ofthe quartic and the quintic using several limits (towers of generallyconvergent iterative maps linked serially).”. ... P. Doyle and C. McMullen [24]: “But can be solved in the case ofthe

13 Dec 2018: h(Xn) = z |Sn(xn Xn)3/2. αφ(Xn)δ|. (24). 2. Medium with Linear Profile. ... Reconstruct the surface h(Xn) by eq. (24) for uniformmedium or (26) for linear profile using Φ obtained aboveend for.

10 Mar 2018: A different approach was developed by Painlevé, Kowalevskaya, and Gambier who studied 2ndorder ODEs in the complex domain.16,24. ... Proc. Cambridge Philos. Soc. 156, 99–113. (2014).24 Painlevé, P., “Sur les équations différentielles du

13 Dec 2018: 2.1. Formal solution and splitting series. The method of solution is analogous to that applied to the electromagneticproblem in 2-d or 3-d [23, 24]. ... 24] M. Spivack, J. Ogilvy, C. Sillence, Electromagnetic scattering by large com-plex scatterers in 3d,

19 Jul 2018: Thus the space oforbits of K2 in MC admits a Toda Einstein–Weyl structure [3, 24].• There exists a combination of self-dual two-forms which is degenerate when the harmonic. ... Roy. Soc. A363 (1978) 289–295.24. R. S. Ward, ‘Einstein-Weyl spaces

18 Nov 2018: Doyle and C. McMullen [24]: “But can be solved in the case ofthe quartic and the quintic using several limits (towers of generallyconvergent iterative maps linked serially).”. ... P. Doyle and C. McMullen [24]: “But can be solved in the case ofthe

13 Dec 2018: For scalar wave fields witharbitrary incident angles the scattered field obeys the Helmholtzboundary integral equation [1, 24]. ... Sel. Top. Appl. Earth Obs. Remote. Sens. 7,1573–1583 (2014). 24. J.