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21 Jan 2018: d. dt(γmv) = e(E v B). ——————. (b) [unseen calculation] Suppose that B = 0, that E is constant and that att = 0 the particle has velocity v0. ... d2v. dt2=. e. mγ. dv. dtB =. (e. mγ. )2(v B) B =. (e. mγ. )2(vB2 B(v B)). In terms of the

29 Nov 2018: LEMMA 5.2 (Dümbgen, Samworth and Schuh-macher, 2011). Let P Pd , let φ := log ψ (P ),and let P (B) := B eφ for any Borel set B Rd. ... P (B) =d. j =1Pj. (w j B. ) B Bd ,for some W = (w1,. ,

3 Oct 2018: 1(x is a trifurcation).  c |B(n)| = c (2n 1)d. ... B(k,) = [, (2k 1)] [,]. and B(,) = B() = [,]2.

14 Jul 2018: There exists B = B(D,R, ) (0,) such that,for G′ GD,R satisfying δG′ ,. (5.4)µ(G). f(K L) β(G′) = µ(G′), if K = K(G,G′) > ... 2dn 1). eAnβn,. as required. Proposition 7.4. There exists B = B(d,r,δG) > 0, that is non-decreasing in d, r,and

4 Jan 2018: N1 if B B(s, a, b, t),N1 if B B(s, b, a, t),. ... A B B. C C. r1. r′1r2. r′2 r′3. r3. A.

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.

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.

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: 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: 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).