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27 Mar 2022: We write. 𝐞. a. ′′. =. R. 1. (. θ. ). a. b. 𝐞. b. ′. with. R. 1. (. θ. ). =. (. 1. 0. 0. 0. cos. θ. sin. θ. 0. -. ... V. eff. (. θ. ). =. I. 1. (. b. -. a. cos. θ. ). 2. 2. sin. 2. θ. M. g.

18 May 2022: uU0 sin b cos h. pr0r. 2. þX1n2. sin nb cos nhpn. ... Pane, and B. Nelson, “Soft microma-chines with programmable motility and morphology,” Nat.

27 Mar 2022: θ. =. -. (. g. /. l. ). sin. θ. ,. T. =. m. l. θ. ˙. 2. m. g. cos. θ. ... 2. sin. 2. θ. ). m. g. l. cos. θ. Notice that the coordinate.

10 May 2022: µs(θ)=. l=0. µslPl(cos θ), µp(θ)=. l=0. µplPl(cos θ). (2.8a,b). In the case of our spherical particle, the slip velocity due to either one ... s0 =sb(rc)r sR3. 2r2(sz cos θ s. y sin θ sin φ).

27 Mar 2022: R. cos. (. ω. (. t. -. t. 0. ). ). (4.299). with. a. ,. b. ,. R. and. t. 0. integration constants. ... A. cos. (. ω. (. t. -. t. 0. ). ). and. p. =. -. m. ω. A. sin. (. ω. (.

3 Dec 2022: with. @B. @t=. @E. @x= kE0 cos(kx! t). We find. B =E0c. ... E = cos(k x! t) sin(k x! t). with Maxwell equations ensuring that k = k = 0.

3 Dec 2022: EI. ET. B. B. BR. I. T. Figure 66: Incident, reflected and transmitted waves with normal polarisation. ... E(x, t) = E(!) ek2z cos(k1z! t). B(x, t) =|k|! (ẑ E(!)) ek2z cos(k1z!

18 May 2022: 2A0A(cos(2ϕ1) cos(2ϕ2)) 0. 0 0. ) O((πN)1), (S37). Ĉ2 = 1. ... 0)2 ) η cos(ϕ. (0)2 ), (S46). and is obtained by multiplying Eq.

10 May 2022: 2A0A(cos(2ϕ1) cos(2ϕ2)) 0. 0 0. ) O((πN)1), (S37). Ĉ2 = 1. ... 0)2 ) η cos(ϕ. (0)2 ), (S46). and is obtained by multiplying Eq.

16 Sep 2022: 00 = 30. r) = A. B. r2. The first term is just a constant rotation, while. ... 21. R22 R21. and B = (1 2)R21R. 22. R22 R21.

10 May 2022: e1 = cos χ [cos θ (cos φex sin φey) sin θez] sin χ [sin φex cos φey] , (1). ... e2 = sin χ [cos θ (cos φex sin φey) sin θez] cos χ [sin φex cos φey] , (2).

21 Oct 2022: x′ = x cos ωt y sin ωt. y′ = y cos ωtx sin ωtz′ = z (2.18). ... 12ml2θ̇2 mgl cos θ (2.39). From which we may derive Lagrange’s equations using the coordinate θ directly.

21 Oct 2022: x′ = x cos ωt y sin ωt. y′ = y cos ωtx sin ωtz′ = z (2.18). ... 12ml2θ̇2 mgl cos θ (2.39). From which we may derive Lagrange’s equations using the coordinate θ directly.

21 Jul 2022: qI (x, y) = eik0x cos θik0y sin θ (2.3). corresponding to a wave incident at angle θ measured in the anti-clockwise direction from the positivex-axis. ... q(r, θ ) eik0r sin θ. k02π r. γ. eik0x cos θ q(x, 0+)dx, as r , (5.2).

20 Jul 2022: Forthis, the signal length N =4000 is divided into 10 pieceswith corresponding functions randomly selected from theset F(x) = {b sin(2πax), ax, ax b, b cos(2πax)} and ran-domly ... Signal Process.,vol. 58, no. 6, pp. 3042–3054, Jun. 2010. [30] B.

30 Mar 2022: The eigenvalue equation is. y′′ λy = 0 , (1.19a). with general solutiony = A cos λ. ... Thereforey(x) = Aex/2 cos. λx Bex/2 sin. λx ,. where A and B are constants.

28 Feb 2022: B to ρ and J. In modern notation, Maxwell’s equations are:7. ... Reall. that the ẋ B term is second order and can be neglected.