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28 Oct 2020: For instance: choosinga(x ) = f (x ) = cos πx , b(x ) = sin 2πx (which incidentally evenleads to a sparse matrix) we get. ... Tn(x ) := cos n arccos x, x [1, 1],. or, in a more instructive form,.

19 Oct 2020: 12µ 1. . The matrix A is normal, with the eigenvalues λ = 1 iµ cos πh(see Example 2.15), so that ‖A‖2 = 1 µ2, hence instability for anyµ. ... By Exercise 4, its eigenvalues and orthonormal eigenvectors aregiven as. B q = λq

11 Nov 2020: x(t) = X R sin(!B(t t0)) and y(t) = Y R cos(!B(t t0)). ... AN=. g. 4r. 1 cos. sin(1.25). The resulting magnetic field is.

5 Feb 2020: Sébastien Michelin, a Simon Game,b Eric Lauga, c Eric Keaveny b andDemetrios Papageorgiou b. ... usingsinh(iz) = i sin z and cosh(iz) = cos iz.

5 Feb 2020: PnmdyðfC0. sin f. cos f. 0. 0BBB@. 1CCCAeimfdf:. (29). The components of the angular velocity are. ... 1). Fig. 4 Concentration distributions: quantitative comparison of theory(solid curves) and simulations (symbols) for the asymmetric (black circles,k0

8 Sep 2020: 2(B) and2(C)] and starts propagating from head (tapered end) to tail at speed v0 = vk cos(φ ) = vk sin(θ /2),which is the projected speed on the axis ... K̃13 = d3β sin θ , (40)K̃23 = 3 (d cos θ 3/2), (41).

14 Dec 2020: 2. (14). Finally we define the vector t = ( cos θ , 0, sin θ ). An illustrative sketch is provided in Fig. 3(b).The flow component of interest for direct interactions, which ... 2, 0, cos θ. 2. ), (28). and 1 < δ < 0 for R > 1.

22 Sep 2020: φp. 0–π π. x2. x1x3. ds/dt. –0.4 0.40. (a). (b). (c). ... x1. 6. 4. 2. 0–1–2 21. x3. x1. (a). (c). (b).

5 Oct 2020: φ = U(r a2/r) cos θ,. with associated streamfunction. ψ = U(r a2/r) sin θ,. ... As before. u. t= ν. 2u. y2in y > 0. u = U cos ωt on y = 0.

24 Nov 2020: 12k. {. [. (b l sin θ1 l sin θ2)2 (l cos θ2 l cos θ1)2]1/2. ... the directions (1, 0), ( cos 60, sin 60), ( cos 60, sin 60), i.e.