What is Jacobi: Definition and 59 Discussions

Sir Derek George Jacobi (; born 22 October 1938) is an English actor and stage director. A "forceful, commanding stage presence", Jacobi has enjoyed a successful and distinguished stage career, appearing in various stage productions of William Shakespeare such as Hamlet, Much Ado About Nothing, Macbeth, Twelfth Night, The Tempest, King Lear, and Romeo and Juliet. He is also known for his performances in Anton Chekov's Uncle Vanya and Edmond Rostand's Cyrano de Bergerac. He was given a knighthood for his services to theatre by Queen Elizabeth II in 1994 and is a member of the Danish Order of the Dannebrog.
In addition to being a founder member of the Royal National Theatre and winning several prestigious theatre awards, Jacobi has also enjoyed a successful television career, starring in the critically praised adaptation of Robert Graves's I, Claudius (1976), for which he won a BAFTA; in the titular role in the medieval drama series Cadfael (1994–1998), as Stanley Baldwin in The Gathering Storm (2002), as The Master in Doctor Who (2007), as Stuart Bixby in the ITV comedy Vicious (2013–2016) and as Alan Buttershaw in Last Tango in Halifax (2012–present). In 2019, he played Edward VIII, the Duke of Windsor, in the third season of the critically acclaimed Netflix series The Crown.Though principally a stage actor, Jacobi has appeared in a number of films, including Othello (1965), The Day of the Jackal (1973), Henry V (1989), Dead Again (1991), Gladiator (2000), Gosford Park (2001), Nanny McPhee (2005), The Riddle (2007), The King's Speech (2010), My Week with Marilyn (2011), Anonymous (2011), Cinderella (2015), and Murder on the Orient Express (2017).
He has twice been awarded a Laurence Olivier Award, first for his performance of the eponymous hero in Cyrano de Bergerac in 1983 and the second for his Malvolio in Twelfth Night in 2009. He also received a Tony Award for his performance in Much Ado About Nothing in 1984. Jacobi has also received two Primetime Emmy Awards for Outstanding Supporting Actor in a Miniseries or Movie for The Tenth Man (1988), and Outstanding Guest Actor in a Comedy Series for Frasier (2001). Jacobi has also earned two Screen Actors Guild Awards along with the ensemble cast for Robert Altman's Gosford Park (2001), and Tom Hooper's The King's Speech (2010).

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  1. Lexaila

    Quadratic Residue and Quadratic Reciprocity Law QRL

    (p-6/p)=(-1/p)(2/p)(3/p) Make a table, so at the head row you have p(mod24), (-1/p), (2/p), QRL+-, (p/3) and finally (p-6/p), with in the head column below p (mod 24): 1,5,7,11
  2. N

    Fortran Need help with Jacobi relaxation method for Dirichlet boundary conditions

    program r_jacobi implicit none !!!!Variables!!! real*8 V, V_1, V_2, Lx, Ly integer n ,i , j, k, nx, ny real*8, allocatable :: arrx(:), arry(:), phi(:,:,:) real*8 x, xi, xf, y, yi, yf, dx, dy real*8 d, q, bx, by V=1 V_1=V V_2=-V Lx = 2 Ly = 1 nx = 200 ny = nx/2...
  3. L

    I Jacobi identity of Lie algebra intuition

    My intuition about the Lie algebra is that it tries to capture how infinitestimal group generators fails to commute. This means ##[a, a] = 0## makes sense naturally. However the Jacobi identity ##[a,[b,c]]+[b,[c,a]]+[c,[a,b]] = 0## makes less sense. After some search, I found this article...
  4. M

    MHB Fixed point,, Jacobi- & Newton Method, Linear Systems

    Hey! :giggle: Question 1 : Let $g(x)-=x-x^3$. The point $x=0$ is a fixed point for $g$. Show that if $x^{\star}$ is a fixed point of $g$, $g(x^{\star})=x^{\star}$, then $x^{\star}=0$. If $(x_k)$ the sequence $x_{k+1}=g(x_k)$, $k=0,1,2,\ldots$ show that if $0>x_0>-1$ then $(x_k)$ is...
  5. L

    I Jacobi Fields & Tidal Forces

    Given a one parameter family of geodesics, the variation vector field is a Jacobi field. Mathematically this means that the field, ##J##, satisfies the differential equation ## ∇_{V}∇_{V}J =- R(V,J,)V## where ##V## is the tangent vector field and ##R## is the curvature tensor and ##∇## is the...
  6. B

    A Jacobi Elliptic Functions and Integrals

    Are there any useful references or resources that intuitively show how Jacobi Elliptic functions [sn, cn, dn, etc] are geometrically interpreted from properties of ellipses? And how the Jacobi Elliptic functions and integrals can be shown to be generalizations of circular trig functions? Thanks!
  7. mishima

    Sn(u), Jacobi elliptic function, for simple pendulum of any amplitude

    I understand how to reach $$\int_0^\phi \frac{d\theta}{\sqrt{1-k^{2}sin^{2}\theta}}=\sqrt \frac g l t$$ from physics but from there I don't get how to turn that into this new (for me) sn(u) form.
  8. D

    Hamilton Jacobi equation for time dependent potential

    Homework Statement Suppose the potential in a problem of one degree of freedom is linearly dependent upon time such that $$H = \frac{p^2}{2m} - mAtx $$ where A is a constant. Solve the dynamical problem by means of Hamilton's principal function under the initial conditions t = 0, x = 0, ##p =...
  9. darida

    A First Variation of Jacobi Operator

    <Moderator's note: Moved from a homework forum.> Homework Statement From this paper. Let ##L## be the Jacobian operator of a two-sided compact surface embedded in a three-maniold ##(M,g)##, ##\Sigma \subset M##, and defined by $$L(t)=\Delta_{\Sigma(t)}+ \text{Ric}( ν_{t} , ν_{t}...
  10. B

    I What are the definitions of Jacobi Elliptic Functions?

    When doing a problem on a pendulum undergoing elliptical motion, I came across sn(z), which is apparently a "Jacobi Elliptic Function". When I looked into it further, I saw that these functions are essentially circular trigonometric functions but about an ellipse instead of a perfect circle. Can...
  11. V

    Hamilton - Jacobi method for a particle in a magnetic field

    Homework Statement Hamiltonian of charged particle in magnetic field in 2D is ##H(x,y,p_x,p_y)=\frac{(p_x-ky)^2+(p_y+kx)^2}{2m}## where ##k## and ##m## are constant parameters. For separation of this system use ##S=U(x)+W(y)+kxy+S_t(t)##. Solve Hamilton - Jacobi equation to get ##x(t), y(t)## ...
  12. S

    Is this solution accidentally using Jacobi method instead of....

    Homework Statement The problem is attached. Homework Equations Isolating each x_i. The Attempt at a Solution I watched this video for the Jacobi method.: I also watched this video for the Gauss-Seidel method.: At least based on the videos mentioned above, it seems that the difference...
  13. J

    Classical mechanics: Jacobi variational principle

    An isolated mechanical system can be represented by a point in a high-dimensional configuration space. This point evolves along a line. The variational principle of Jacobi says that, among many imagined trajectories between two points, only the SHORTEST is real and is associated with situations...
  14. binbagsss

    Periods of Jacobi Elliptic functions

    Homework Statement I have that ##(\psi(z)-e_j)^{1/2}=e^{\frac{-n_jz}{2}}\frac{\sigma(z+\frac{w_j}{2})}{\sigma(\frac{w_j}{2})\sigma(z)}## has period ##w_i## if ##i=j## and period ##2w_i## if ##i\neq j## where ##i,j=1,2,3## and ##w_3=w_1+w_2## (*) where ##e_j=\psi(\frac{w_j}{2})## I have...
  15. binbagsss

    Jacobi Theta Function modularity translation quick q

    Homework Statement I have the Jacobi theta series: ##\theta^{m}(\tau) = \sum\limits^{\infty}_{n=0} r_{m}(\tau) q^{n} ##, where ##q^{n} = e^{2\pi i n \tau} ## and I want to show that ##\theta^{m}(\tau + 1) = \theta^{m}(\tau) ## (dont think its needed but) where ##r_{m} = ## number of ways of...
  16. Clarence Liu

    Using Mathematica to solve for Jacobi Identity

    Hi everyone, I'm new to Physics Forums and to Mathematica, as well as Jacobi Identity. In any case, I was wondering on how I may use Mathematica to solve various Quantum Mechanics related problems through commutators. Like if it's possible to find out what is the form of a particular commutator...
  17. C

    How Does the Hamilton-Jacobi Equation Describe Particle Motion in a Plane?

    Homework Statement The motion of a free particle on a plane has hamiltonian $$H =E = \text{const} = \frac{1}{2m} (p_r^2 + \frac{p_{\theta}^2}{r^2})$$ Set up and find a complete integral for ##W##, the time independent generating function to canonical coordinates such that new coordinates are...
  18. K

    Jacobi elliptic functions with complex variables

    I am trying to solve a Duffing's equation ##\ddot{x}(t)+\alpha x(t)+\beta x^3(t)=0## where ##\alpha## is a complex number with ##Re \alpha<0## and ##\beta>0##. The solution can be written as Jacobi elliptic function ##cn(\omega t,k)##. Then both ##\omega## and ##k## are complex. The solution to...
  19. B

    Power flow studies using Jacobi and Gauss Seidel

    I have been asked to solve the actual load flow distribution in a given power network using two iterative methods. I have chosen Jacobi and Gauss Seidel. we have to use MATLAB to find where the solution converges. I am fine with all of this, but we have been tasked with providing graphical...
  20. nxtgarnett

    Jacobi and Gauss-Seidel Iteration

    For the Matrix 1 2 -2 1 1 1 2 2 1 What is the spectrum for the Jacobi iteration matrix and the Gauss-Seidel iteration matrix. And are the methods convergent?
  21. Th3HoopMan

    Correlation between Iterative Methods and Convolution Codes

    Hey guys so I have this Calc 3 project and the end is throwing me for a loop. I've done the encoding part, and I've coded the standard iterative methods, but I don't see how the two correlate so I can use the iterative methods to decode a "y stream" with the inputs specified...
  22. H

    Looking for an example of a Successive over-relaxation

    Hi I am working on a programming assignment that requires me to implement the successive over-relaxation algorithm. We are given the wikipedia page for this: http://en.wikipedia.org/wiki/Successive_over-relaxation. I have read through the wikipedia page for this numerous times but am still...
  23. Matterwave

    Are Jacobi fields defined at intersection points?

    I have some questions with regards to conjugate points on a congruence of time-like geodesics (will be referring to Wald 9.3 throughout). First, we define ##\gamma## to be a time-like geodesic with tangent ##\xi^a## parametrized by ##\tau## and with ##p\in\gamma##. We consider the "congruence of...
  24. MathematicalPhysicist

    Schouten identity resembles Jacobi identity

    Am I the only one who sees the resemblance between these two identities? Schouten: <p q> <r s> +<p r> <s q>+ <p s > <q r> =0 Jacobi: [A,[B,C]]+[C,[A,B]]+[B,[C,A]]=0 In Schouten the p occours in each term in the three terms, so we can regard it as dumby variable, and somehow get a...
  25. J

    Complementary jacobi amplitude

    I found this identity in the wiki https://de.wikipedia.org/wiki/Jacobische_elliptische_Funktion#Abstrakte_Definition_als_spezielle_meromorphe_Funktionen One propertie of the ellipitc integral is: K(k') = K'(k), all this set of ideia seems answer an old doubt, ie, exist a complementary...
  26. C

    Jacobi identity for covariant derivatives proof.

    Suppose we have a torsion free connection. Does anyone here know of a slick way to prove that covariant derivatives satisfy the Jacobi identity? I.e. that $$([\nabla_X,[\nabla_Y,\nabla_Z]] + [\nabla_Z,[\nabla_X,\nabla_Y]] +[\nabla_Y,[\nabla_Z,\nabla_X]])V = 0$$ without going into...
  27. P

    Use the Jacobi identity to show Lie algebra structure constant id.

    Homework Statement Use the Jacobi identity in the form $$ \left[e_i, \left[e_j,e_k\right]\right] + \left[e_j, \left[e_k,e_i\right]\right] + \left[e_k, \left[e_i,e_j\right]\right] $$ and ## \left[e_i,e_j\right] = c^k_{ij}e_k ## to show that the structure constants ## c^k_{ij} ## satisfy the...
  28. quasar987

    Jacobi identity in local coordinates?

    Jacobi identity in local coordinates?!? Apparently (i.e. according to an article written by physicists), the Jacobi identity for the Poisson bracket associated to a Poisson bivector \pi = \sum\pi^{ij}\partial_i\wedge\partial_j is equivalent to...
  29. A

    Lagrangian and Jacobi Integral

    Homework Statement A particle of mass m moves on the surface of a paraboloidal bowl with position given by r=rcosθi+rsinθj+\frac{r^{2}}{a}k with a>0 constant. The particle is subject to a gravitational force F=-mgk but no other external forces. Show that a suitable Lagrangian for the system is...
  30. Coelum

    Inverse Jacobi Matrix in Spherical Coordinates

    Dear all, I am reading R.A. Sharipov's Quick Introduction to Tensor Analysis, and I am stuck on the following issue, on pages 38-39. The text is freely available here: http://arxiv.org/abs/math/0403252. If my understanding is correct, then the Jacobi matrices for the direct and inverse...
  31. S

    Jacobi method and Gauss-Seidel method ,

    Homework Statement for part c , it asked for showing both 2 method converge for any initial condition. I think we can show that by using $$ρ(T_{j}), ρ(T_{g}) <1 $$ I want to know whether it's correct or not , and is there any faster method? Homework Equations $$ρ(A)$$ means spectral...
  32. J

    Jacobi Sums Explained: A Simple Guide with Examples

    Would someone be kind enough to explain Jacobi sums in a simple manner using actual numbers. I have read over the math jingo 100 times and have no clue what it actually does. Thanks! Edit: Here is a link to the wiki of the Jacobi sums. http://en.wikipedia.org/wiki/Jacobi_sum
  33. M

    Understanding the Hamilton-Jacobi Equation in Conservative Systems

    Hello! General Question about the H-J equation. What are the steps to be followed if we are in a conservative system? And while answering my question, please in the step after we find S, and when you derive S wrt alpha and place it equals to β. When is alpha Energy? When it is not? i.e is it...
  34. A

    Jacobi method convergence for hpd matrices

    Homework Statement Let A be a squared, hermitian positive definite matrix. Let D denote the diagonal matrix composed of the diagonal elements of A, i.e. D = diag((A)11,(A)22,...(A)nn). Prove that if the Jacobi iterative method converges for A, then 2D - A must also be hermitian positive...
  35. I

    Proving the Jacobi identity from invariance

    "Proving" the Jacobi identity from invariance Hi all, In an informal and heuristic manner, I have heard that the "change" in something is the commutator with it, i.e. \delta A =[J,A] for an operator A where the change is due to the Lorentz transformation U = \exp{\epsilon J} = 1 + \epsilon J...
  36. J

    Writing a recursive function to compute the Jacobi symbol

    Write a recursive function to compute the Jacobi symbol J(a, n), is defined for relatively prime integers a and n, a> o, \mbox{ and } n > 0 by the formula J(a, n) = 1 \mbox{ if a = 1, } = J(a/2, n)*(-1)^\frac{n^2-1}{8} \mbox{ if a is even, } =J(n \% a, a)*(-1)^\frac{(a-1)*(n-1)}{4} \mbox{...
  37. K

    Jacobi Matrix and Multiple Intgrals

    Homework Statement Let D be the set of points (x,y) in R^2 for which 0 is ≤ x ≤ 1 and 0 ≤ y ≤ 1. Find a function g: R^2 --> R for which: ∫_0^1 ∫_0^1 h(x,y)dxdy = ∫_0^1∫_0^1 h(y^5, x^3) * g(x,y)dxdy is true for all functions h: D--> R integrable over D In the question before this I...
  38. A

    What if Jacobi Method's condition did not met?

    what if Jacobi Method's condition did not meet? Homework Statement solve by Jacobi Method upto four decimal places 8x+y-z= 8 2x+y+9z= 12 x-8y+12z = 35 Homework Equations The Attempt at a Solution since the condition of convergence of jacobi method is |A1| > |B1|+|C1|...
  39. K

    How do I Find the Jacobi Matrix and Its Determinant for a Given Transformation?

    Homework Statement The transformation f is defined by: R^2 --> R^2 and is defined by: f(x,y) = (y^5, x^3) Find the jacobi matrix and its determinant Homework Equations f(x,y) = (y^5, x^3) The Attempt at a Solution I would start by differentiating y^5 with respect to x and then y, then...
  40. S

    The Jacobi Iterative method question

    Homework Statement (Ax = B) A: 3.1410 -2.7180 1.4140 -1.7321 9.8690 2.7180 -7.3890 0.4280 2.2360 -2.4490 1.0000 -1.4140 31.0060 7.3890 -2.6450 0.1110 B: 3.316 0 3.141 1.414 The question in my Numerical Methods assignment asks to use the Jacobi Iterative method to solve the system...
  41. O

    Gauss-Seidl, Gauss-Southwell, Jacobi

    Couple of days ago I downloaded a book on numerical optimization, hoping to get clearer picture on some techniques. But, I'm surprised that some of the concepts were not precisely separated from one another. Namely, in the part of "coordinate descent methods" (cdm), I found that, in the...
  42. V

    Prove the chain rule for Jacobi determinants

    Homework Statement Prove the chain rule for Jacobi determinants \frac{d(f,g)}{d(u,v)} * \frac{d(u,v)}{d(x,y)}=\frac{d(f,g)}{d(x,y)} Homework Equations Definition of Jacobi determinant \frac{d(f,g)}{d(u,v)} = \frac{d(f,g)}{d(u,v)} = det \begin{bmatrix} \frac{df}{du}&\frac{df}{dv} \\...
  43. X

    Jacobi, Gauss-Seidel, SOR question

    Homework Statement Evaluate the number of iterations that are needed to have 10^-9 precision with the Jacobi, Gauss-Seidel, and SOR ( with ω=1.5) methods. Compare these 3 methods for different values of n - for instance 3≤n≤20. Plot the convergence curves for the 3 methods for each n. Homework...
  44. A

    Jacobi Vs gauss-seidel

    How we prove that rate of convergence of gauss-Seidel method is approximately twice that of Jacobi iterative method without doing an example itself ? What's the general proof of this statement ? I didn't fin in any book ? Can anyone please help me ?
  45. Z

    Levi-Civita & Jacobi: Meaning & Question

    hey Folks, please have a look at the attached Ex from MTW. does somebody know what is the meaning of the parallel bars in the first levi civita symbol ? Is there a typo in this EX perhaps? I would have expected that on the right hand side one would see the product which is shown in the first...
  46. kreil

    Help with Reducing an Equation into Jacobi Identity Form

    Homework Statement Reduce the equation \partial_\mu {*} F^{\mu \nu} = 0 into the following form of the Jacobi Identity: \partial_\lambda F_{\mu \nu} + \partial_\mu F_{\lambda \nu} + \partial_\nu F_{\lambda \mu} = 0 The Attempt at a Solution I can't figure out what the '*' is supposed to...
  47. A

    Jacobi least time vs. Fermat Hamilton

    Could anyone give me a simple explanation as to why the Fermat/Hamilton principle would be called more general than the Jacobi least time principle? I am trying to understand what differences would result from using the one principle vs. the other; eg: where/in what way would the Jacobi least...
  48. F

    Help - Verify the Jacobi Identity (Arfken)

    Hello, I'm unfamiliar with the notation used in this problem with the commas. I understand matricies, identities, etc. but not sure about the commas.. Question 3.2.9: Verify the Jacobi Identity: [A,[B,C]] = [B,[A,C]] - [C,[A,B]] I see the BAC CAB rule here, but not sure how to show it...
  49. W

    Using the Theta Function to Solve for a Jacobi-Related Equation

    I was reading a book on the zeta function and came across this attributed to Jacobi. I have no idea where to find a source about this so maybe someone can give me some direction. Let \psi(x) = {\sum}^{\infty}}_{n=1}e^{-n^2 \pi x}. How do you show that \frac{1+2\psi(x)}{1+2\psi(1/x)} =...
  50. G

    Jacobi Iteration Homework: Solving System of Equations

    Homework Statement consider the systems of equations 2x1 - x2 = 1 -31 + 4x2 =11 a) determine the ixact solution? b)apply jacobi iteration.Does the matrix C satisfy the required condition? c)starting with x(0) =( \stackrel{1}{1} ) calculate x(1) and x(2) and the prior error bound for x(2)...