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17 Sep 2020: 2. Prove the formula sin(A B) = sin A cos B cos A sin B. ... a b c)2 = a cos A b cos B c cos C.

10 Mar 2020: ȧ. a= ḃ. b= S sin θ cos θ, θ̇ =. S(b2 cos2 θ a2 sin2 θ)a2 b2. Combine these effects to obtain. ... ȧ. a= ḃ. b= S sin θ cos θ,. θ̇ =S(b2 cos2 θ a2 sin2 θ).

27 Feb 2020: 2 S)zByBz. Bx. Bz. K cos(Kz). sin(Kz+) 1. z+. ,. vy = v2az2. ... BxBz. K cos(Kz). sin(Kz+). The meridional (x and z) components of B are called the poloidal magnetic field, while the azimuthal(y) component is called the toroidal magnetic field.

4 Feb 2020: in Ow(l i)]B 1 •- ,. cos cos cos k2• sin 20.• -k} cos 20.,)A• iT.,•, 2k•, cos. ... d{ - 3a./.} cos X sin Or,( 1 i) - 2iR•vki, cos Ov] B•.

20 Oct 2020: So it's trying to get more air in and it can't cos that's [the plunger] there. ... 4. Teacher: Cos normally if something's doing the pulling. 5. Jamie: Mmm.[7 seconds].

23 Dec 2020: vr = rν cos φ[c(ν 1)Pν1 b(ν 1) cos θ Pν. ], ... 2.12a). vθ = rν cos φ[cP′ν1 2a csc θ Pν b.

7 Dec 2020: h) y = sin(4x2 π/2). (i) y = cos(2|x|). G H I. ... a)1. (ex)y= exy. (b) 2exy 2eyx = (ex ex)(ey ey) (ex ex)(ey ey).

26 Oct 2020: Substituting y,a,b and f by theirFourier series and using (3.3)-(3.5) we obtain an infinite dimensional system of linear equationsfor the Fourier coefficients ŷn:. ... For instance: choosinga(x) = f(x) = cos πx, b(x) = sin 2πx (which incidentally

24 Aug 2020: G. J. CONDUIT AND P. D. HAYNES PHYSICAL REVIEW B 78, 195310 2008. ... DIFFUSION MONTE CARLO STUDY OF A VALLEY-… PHYSICAL REVIEW B 78, 195310 2008.

20 Oct 2020: I said does it change its weight. S: Er, no, cos you haven’t took anything off it, it’s just a different shape. ... B/S]. A student expressing view to a discussion topic and backing it up:.

24 Aug 2020: the gauge field as A = 2ih̄〈χ |χ 〉 = h̄ cos θ φ̂/ρ. ... Finally, we compare thepredictions for the gauge field realized by the proposed lasersetup, A = 2h̄ cos θ φ̂/ρ [Figs.

16 May 2020: Other fascinating applications include quantum teleportation – which in prin-ciple gives a way of effectively deleting a physical system at A and recreatingit at B without sending it along a path ... from A to B – and other types ofquantum

3 Jan 2020: Other fascinating applications include quantum teleportation – which in prin-ciple gives a way of effectively deleting a physical system at A and recreatingit at B without sending it along a path ... from A to B – and other types ofquantum

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).

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.

4 Nov 2020: r =λ. e cos θ 1 ,. where λ and e are non-negative constants. ... I(x) =. 3π. 0. e(tx cos t) dt. (b) Find the first two leading nonzero terms of the asymptotic expansion, as x , of theintegral.

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.

28 Jun 2020: θ = H0 η (m,0 1)1/2 (15.2). 3. whereby:r(θ) = A(1 cos θ) (15.3). ... m,0 1(15.7). and, more generally,r. rmax=. 1. 2(1 cos θ). (15.8).

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.

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

12 Oct 2020: Thus, the linear system Au = b can be written explicitlyin the block form. ... By Exercise 4, its eigenvalues and orthonormal eigenvectors aregiven as. B q = λq, λ = 4 2 cos πm1,.

2 Mar 2020: Prove that its circumference is 2π sin(ρ)and that it bounds a disc on S2 of area 2π(1 cos(ρ)).(b) Let C h be a hyperbolic circle with ... distinct points in the sphere.(b) Construct a non-orientable compact hyperbolic surface.

7 Apr 2020: Φ A BI(D) cos x4. (1). with A = 0 and B = 1 for randomly oriented flakes and A = 1and B = 0 for a perfect alignment. ... Carbon 2007, 45, 821827.(16) Wang, L. L.; Tay, B. K.; See, K.

18 Sep 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.

13 May 2020: 220. (|A|2 3. 4x20. ),. εv =1. 220(Br sin 0t Bi cos 0t)2. ... 1. 220(Br cos 0t Bi sin 0t). 2. =1. 220|B|2,. as required.

23 Dec 2020: Online version in colour.). (b). (c). – a2a2 a. x. –1.0–0.5. ... c (x,. y,x). Figure6. (a)Three-,(b)two-and(c)one-dimensionalplotsoftheoscillatorypartoftheelectronclouddensity,ρoscE (x, y, z) =[cos(kx) cos(ky) cos(kz)]/3 with k = 2π/a, for the

4 Nov 2020: 1. 2I3. (ψ̇ φ̇ cos θ. )2 Mgl cos θ. ... V = V0(. cos(x) cos(2x)),. with positive constant V0. i) For very small V0, use the nearly-free electron model to compute explicitly the lowest-energy band gap to leading

9 Jan 2020: K. We. now introduce some notation to simplify (44):. cosa = cos(2πa/K) = <[ca] for integer a, (45). ... mod K and cosa = cos(a+ K2. ) mod K, noting that K is a.

24 Aug 2020: IV B we studythe temperature-dependent current in a Josephson junction.In Sec. ... no additional resistance.The current J (T ) = JJ(T ) cos(φL φR) is maintained by the.

24 Aug 2020: drops, Phys. Rev. B, 78:035111, 2008 [1]. Chapter 3: G.J. Conduit and P.D. ... The energy spacing between the channels can be controlledby an external magnetic field B.

3 Oct 2020: 4. (a) Simply-supported wooden panel painting (b) Rigidly supported wooden panel painting. ... where r = eilnr = cos(lnr) i sin(lnr), and is the oscillatory index defined as.

24 Jul 2020: Figure 5(a), and of β̄2/β̄1 = 10, see Fig-ure 5(b). ... σyy iσxy =K2πr. ri , (28). where r = eilnr = cos(lnr) i sin(lnr), and the oscillatory index is defined as.

12 Feb 2020: Hence show that, for large Reynolds number, an energy amplification of(cos θ. ... ȧ. a= ḃ. b= S sin θ cos θ ,. θ̇ =S(b2 cos2 θ a2 sin2 θ).

7 Oct 2020: Thus, the linear system Au = b can be written explicitlyin the block form. ... By Exercise 4, its eigenvalues and orthonormal eigenvectors aregiven as. B q = λq, λ = 4 2 cos πm1,.

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.

25 Feb 2020: P. Kelly (Department of Pure Mathematics and Mathematical Statistics,. University of Cambridge)B. ... Castillo, U. Einmahl, D. Gauthier, D. Heydecker,K. Ray, J. Söhl and B.

4 Nov 2020: i) Calculate e. x2dx. [2]. (ii) Calculate the area enclosed by the curve r = a(1 cos θ), 0 6 θ < 2π, where a > 0. ... cos θ, sin θ,b/a)dr and r(sin θ, cos θ, 0)dθ. where r, θ and z are the usual cylindrical polar coordinates.

22 Jan 2020: Consider the matrix representation of the Euclidean group E(2) in twodimensions  cos θ sin θ asin θ cos θ b. ... a cos ψ sin θ. b+ sin ψ. 1. l. θ.

15 Oct 2020: S =. α β. β α. β. β α.  ,are given by λk = α 2 iβ cos kx , and wk = (i. ... λk (A) =λk (C ). λk (B )=. 1 12 iµ cos kx.

12 Oct 2020: S =. α β. β α. ββ α.  ,are given by λk = α 2 i β cos kx, and wk = (im sin kmx)Mm=1, where x = πh =. πM1. So, all ... λk(A) =λk(C). λk(B)=. 1 12 i µ cos kx. 1 12 i µ cos kx |λk(A)| = 1, k = 1.M.

28 Sep 2020: z = r cos θ. Then compute the Christoffel symbols by directly applying (1.8). ... l2(1 e cos φ) (4.16). where e is the eccentricity, a free parameter.

9 Oct 2020: S =. α β. β α. β. β α.  ,are given by λk = α 2 i β cos kx , and wk = (i. ... λk (A) =λk (C ). λk (B )=. 1 12 i µ cos kx.

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).

26 Oct 2020: y ′′ a(x )y ′ b(x )y = f (x ), y (1) = y (1), (6). ... For instance: choosinga(x ) = f (x ) = cos πx , b(x ) = sin 2πx (which incidentally evenleads to a sparse matrix) we get.

4 Nov 2020: with points . (2 cos v) cos u. (2 cos v) sin u. ... Your mission is to reach the point(x,y) = (B cos α,B sin α), where B > 0.

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.

2 Dec 2020: ii) If a G then e a = a. (iii) If a,b,b′ G are such that a b = e and a b′ = e, then b = b′. ... A group (G, ,e) is abelian2 if for all a,b G we have a b = b a.

7 Jul 2020: cosI = cos Ib cos Ic sin Ib sin Ic cos (b c). ... thedirection of its angular momentum vector) without knowl-edge of c. In fact, the only unknown is c, which can rangefrom 02π, meaning that cos(b c) can range from -1

21 Oct 2020: By Exercise 4, its eigenvalues and orthonormal eigenvectors aregiven as. B q = λq, λ = 4 2 cos πm1,. ... 25 / 28. Splitting of inhomogeneous systems. Note that our analysis should accommodate b = b(t ), sinceboundary conditions might vary in time!

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,.