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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).

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.

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.

16 Jul 2018: U,. (5)b. b i. N. i i1. f. ω ϒ. . ... Rev. Fluid Mech. 48, 105–130 (2016). 19. Keller, J. B. & Rubinow, S.

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‖.

21 Apr 2018: Remark 1 Note that another variant of the splitting can be obtained by swapping thechoices of A and B. ... Comput. Phys. 230(15), 5930–5956. Compact schemes for laser-matter interaction 13. Amstrup, B., Doll, J.

27 Jan 2018: d B dB' _ - B --B '. Aus dieser und aus der zuletzt gefundenen Gleichung folgt aber J = J '. Es ist somit erwiesen, da0 J weder von F noch von. ... 8 (P 4 - B Gmmm a x. oder a v - D- 8 X.

23 Jan 2018: f. (. b. )ZA,b. b=0. (1.112). 12. We can simplify this straight away by substituting in our previous result (1.104). ... b̄,. b. )ZB,b. b=0. (1.122). One finds that⟨ziz̄j⟩ = B1ij , (1.123).

3 Apr 2018: B The group GC0 105. C Frobenius manifolds and hydrodynamic-type systems 107. ... C. (|Dφ|2. Dφ2)]ωΣwhere. B = 2ifww/is the magnetic field on Σ.

26 Apr 2018: Exercises. Matlab has multiple multiplications. As an exercise try the following:>> A=[1,2]>> B=[-3,-4]’>> E=[5,-6];>> AB>> BA>> A.B>> B.A>> AE>> EA>> A.E>> ... However, normally a b = b a and ab = ba.

19 Jul 2018: Moreover, the limit when b or c tends to zero gives a dyon. ... Global Anal. Geom. 38 (2010). 77–92.17. B. E. Niehoff and H.

22 Jan 2018: b "arctan ðcos2 W þ q sin2 WÞR. 2ð1 " qÞsin W cos Wh! : ... Torques computedusing the analytical model (RFT, a) and the numerical model (SBT, b).

19 Jan 2018: are described (at least locally) by functions such as V µ, ̇, B[µ] and ̇µ with various types. ... Hilbert space’ L2(C[B], dµ) for functions on the infinite–dimensional space of boundaryfield configurations C[B].

1 Nov 2018: Note that. [A0, B0] = [U 1AU, U 1BU ] = U 1[A, B]U , (4.15). ... 26 –. where in the second equality we used the fact that a b = b a, stating that the order.

14 May 2018: The Faddeev–Popov. determinant is then. f = detf a[A(x)]. b(y), (8.22). ... 2g2YM. Z. Ntr(E E B B) dd1x = 1. 2. Z.