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13 Dec 2018: erf. [. A. B. AX. B. )]. B. AX. (. erf. ). A. AX. (. erf. [. A. B. AX. B. )]. ... 1. (. t. y. D. x. Q. -. =. where A=a/(2((Kt)), B = b//(2((Kt)) and X = x/a.

24 Jul 2018: a)(a) (b)(b). (c)(c) (d)(d). Fig. 1. (a) 12.5% uniform random subsampling scheme, (b) CS reconstructionfrom uniform subsampling, (c) 12.5% multilevel subsampling scheme, (d) CS ... b}. The kth relative sparsity is. Sk = Sk(N,M,s) = maxzΘ‖PNk1Nk Uz‖.

31 Jan 2018: Details in 1D. d2f. dx2= ρ in a < x < b, with f (a) = A and f (b) = B,. ... where ρ(x),A and B given. Divide [a,b] into N equal segments h = (b a)/N.Use linear finite elements with basis functions.

13 Dec 2018: there. exists p, say, such that p _-> V {P2,Pt} and b o t h ( b , , - b ) p and (be - b)p are. ... a b o v e we can suppose, for each po => pl, that (b - b l ) p l = 0, b y replacing each b.

13 Dec 2018: If AZ issufficiently small so that B is almost constant in Z over thatdistance, say B - B(X), then fz 8z B dZ - AZ B = B', say.Consider the error ... u) = [exp(A' B') - exp(A') exp(B')]ubetween relations (3) and (4).

13 Dec 2018: and B’ = B’({ti}t {pi}) = -c 2 [p(zi - zj) p(yi - yj) - 2p(li - yj)]. ... It. follows that [A, B] is small on the solution space, as required.

13 Dec 2018: curve) from fhe mean surface level. B 58 I B 1 5 8 188 ZSB 18s lines at distances 0. ... 3. 4. -1,s -8 b B 58 I?B IYI 288 2 i Q S88.

13 Dec 2018: exp(B)=1+ B B2. 2! (5). Note that whenK is constant with respect tot , Eq. ... 2. [L,L. t. ](6). (where in general [A, B] denotes thecommutator A B B A of operatorsA and B).

25 Oct 2018: For example, if. f (x) = x2 b2 thenZ. R(x2 b2) (x) dx =. 1. 2|b|[(b) (b)]. (6.25). The previous two results (6.21) & (6.22) can be understood ... m2Z dm Ym(x). then, again exchanging the sums and integrals,. Z b.

13 Dec 2018: z-h(xr)] 2 B. where. X -- X X -- X --2h'(xr)[z-h(x•)],. ... 17), and B = B(x,z,x• ) as in (15). C. Numerical treatment of equations.