Search

14 Nov 2023: 0. (x). 2. Let : [a; b! R be a monotone in reasing with a simple zero ( ) = 0,. ... 0. ( ) 6= 0 for some 2 (a; b). Show that.

26 Feb 2024: S = NkB ln. (. V. N b. ). NkBf(T) ,. where f(T) is some function of temperature. Find F , the free energy of the gas.Determine S and F more explicitly in ... Show that the system undergoes a first order phasetransition at some temperature Tc.

30 Nov 2023: b) A rank-2 Lie algebra has simple roots with coordinates α1 = (1, 0) and α2 =(1, 1). ... ed w. ithou. t per. mis. sion. (b) Show that we may assume Eβ(n1)α = 0 for some integer n.

4 Jan 2024: Show that thissatisfies the relevant boundary condition at the conductor. Find the corresponding magneticfield B. ... Ifthe medium moves with 3-velocity v in some inertial frame, show that the current in thatframe is.

9 Feb 2024: f[0,1,2,4] = 16f′′′(ξ). for some point ξ [0,4]. Note that another proof of this result was given in the lecture on di-vided differences. ... baf(t)dt for some ξ [a,b].). 12. Let f be a function in C4[0,1] and let ξ be any fixed point in [0,1].

23 Oct 2023: b) The physicist Richard Feynman tells the following story:. “I was in the cafeteria and some guy, fooling around, throws a plate in theair. ... Please send any comments and corrections to d.b.skinner@damtp.cam.ac.uk. 4.

2 Aug 2023: b. Explain why A(m) = A(m), and show that the Jacobi identity fixes. ... A(m) = Bm3 Cm,. for some constants B and C. c.

2 Jul 2024: in the spectral lines. He found nothing. Some decades later, in 1896, Pieter Zeeman. ... the Statistical Physics lectures. The term in (4.10) that is quadratic in B is some-.

10 Nov 2023: Multigrid methods The speed of convergence of some iterative methods (Jacobi with relax-ation, Gauss–Seidel, etc.) can be increased drastically when the linear system originates in thediscretization of PDEs, using ... Weassume below that the size of

3 Jun 2024: 147. 17. E. B. Glennie and J. R. Willis, “An Examination of the Effects of some Idealized Models of. ... Trans. R. Soc. A274 (1973) 435-. 491. 23. J. R. Willis, “Some Recent Work in Crack Propagation”, Engng.