Transformation Definition and 1000 Threads

Transformations always give me trouble, but this one does in particular. Assume X_1, X_2 independent with binomial distributions of parameters n_1, n_2, and p=1/2 for each. Show Y = X_1 - X_2 + n_2 has a binomial distribution with parameters n= n_1 + n_2, p = 1/2. My first instinct was...

Homework Statement A spaceship is approaching a planet at a speed v. Suddenly, the spaceship explodes and releases a sphere of photons traveling outward as seen in the spaceship frame. The explosion occurs in the planet frame when the spaceship is a distance L away from the planet. In the...

Hi all, The context of this problem is as follows: I'm trying to implement a discontinuous finite element method and the formulation calls for the computation of line integrals over the edges of the mesh. Anyway, more generally, I need to evaluate \int_{e}f(x,y)ds, where e is a line segment...

I know that every linear transformation from Rn to Rm can be represented in a matrix form. What about a transformation from a 1. Infinite dimension to infinite dimension 2.finite to infinite dimension 3.infinite to finite dimension Can they represented by matrix form...? Before...

Dear All: For a line structure(say a very long atomic chain) and a closed loop structure( connect the head and tail of this atomic chain). Does there exists a transformation between these two structures? For example if we want to study the vibration mode of these two cases. If we already know...

Does there exist a transformation between a line and a closed loop ? Dear All: For a line structure(say a very long atomic chain) and a closed loop structure( connect the head and tail of this atomic chain). Does there exists a transformation between these two structures? For example if we...

Homework Statement Use Y to Δ transformation to find i0 and i/x Homework Equations The Attempt at a Solution Here's my transformation. Calculated i0, which is equal to 3A. I have no clue how to find ix.

Homework Statement Show that Q_{1}=\frac{1}{\sqrt{2}}(q_{1}+\frac{p_{2}}{mω}) Q_{2}=\frac{1}{\sqrt{2}}(q_{1}-\frac{p_{2}}{mω}) P_{1}=\frac{1}{\sqrt{2}}(p_{1}-mωq_{2}) P_{2}=\frac{1}{\sqrt{2}}(p_{1}+mωq_{2}) (where mω is a constant) is a canonical transformation by Poisson bracket test. This...

Homework Statement If \phi \in \mathcal{M} (group of all linear fractional transformations or Mobius Transformations has three fixed points, then it must be the identity. (The proof should exploit the fact that \mathcal{M} is a group. The Attempt at a Solution Hi all, So...

Given the following ODE \[ \left(\frac{du}{dx}\right)^2 = \mu u^2 - \frac{2\alpha}{\sigma + 2}u^{\sigma + 2} - \frac{\gamma}{\sigma + 1}u^{2(\sigma + 1)} \] How do I obtain \[ u(x) = \left(\frac{A}{B + \cosh(Dx)}\right)^{1/\sigma} \] where \(A = \frac{(2 + \sigma)B\mu}{\alpha}\), \(B =...

When performing transformation, after adding SOC media to the newly transformed cells, we place them at 37 degrees Celsius for an hour to allow growth. I understand the need for an incubator but I'm confused regarding how shaking helps in microbial growth? I did some searching on the internet...

Hi everyone, :) Here's another question I encountered recently. I am writing the question and my full solution. Many thanks if you can go through it and find a mistake, or confirm whether it's correct, or can contribute with any other useful comments. :) Problem: Find the matrix of a linear...

I am using an excel sheet to generate some URLs that need a input number encoded. I figured out the pattern -- it is a simple digit manipulation Input --> Encoded Output -------- ---------------------- 271678 --> 01303032373136373875 261268 -->...

Homework Statement Two RVs X1 and X2 are continuous and have joint pdf f_{X_1,X_2}(x_1, x_2) = \begin{cases} x_1+x_2 &\mbox{for } 0 < x_1 < 1; 0 < x_2 < 1 \\ 0 & \mbox{ } \text{otherwise}. \end{cases} Find the pdf of Y = X_1X_2.Homework Equations I'm using the transformation "shortcut' that...

Homework Statement Find the Möbius transformation that maps 0 -> -1 1 -> infinity infinity -> 1 Homework Equations w = f(z) = \frac{az + b}{cz+d} The Attempt at a Solution My first idea was to attempt to solve it as a normal system of eq's but that quickly falls apart due to...

Hi everyone, :) Here's a question I was stuck on. Hope you people can help me out. :) The definition of root vectors is given >>here<<. Now a \(n\times n\) matrix can be diagonalized if it has \(n\) distinct eigenvalues. So I don't see how the given condition (all root vectors are...

Hi everyone, :) Here's a question I got stuck. Hope you can shed some light on it. :) Of course if we write the matrix of the linear transformation we get, \[A^{t}.A=\begin{pmatrix}a_1^2 & a_{1}a_2 & \cdots & a_{1}a_{n}\\a_2 a_1 & a_2^2 &\cdots & a_{2}a_{n}\\.&.&\cdots&.\\.&.&\cdots&.\\a_n...

Hi everyone, :) This is one of those questions I encountered when trying to do a problem. I know that a eigenvector of a linear transformation should be non-zero by definition. So does that mean every linear transformation has eigenvectors? What if there's some linear transformation where no...

Homework Statement Let X_1, X_2 have the joint pdf h(x_1, x_2) = 8x_1x_2, 0<x_1<x_2<1 , zero elsewhere. Find the joint pdf of Y_1=X_1/X_2 and Y_2=X_2. Homework Equations p_Y(y_1,y_2)=p_X[w_1(y_1,y_2),w_2(y_1,y_2)] where w_i is the inverse of y_1=u_1(x_1,x_2) The Attempt at a Solution We can...

This is from a chapter on distributions of two random variables. Let X and Y have the pdf f(x,y) = 1, 0<x<1 and 0<y<1, zero elsewhere. Find the cdf and pdf of the product Z=XY. My current approach has been to plug in X=Z/Y in the cdf P(X<=x) , thus P(Z/Y<=x), and integrate over all values of...

T is a surjective linear transformation T: \mathbb{R^4}-> \mathbb{R^2}. Decide dim ker T. How many free variables do I get if I solve equation system T(x)=y for a vector y \in \mathbb{R^2}? Construct a transformation matrix belonging to a surjective linear transformation...

I have checked many textbooks and papers on SUSY and it seems that none of them mentions anything about the infinitesimal susy transformation on component fields in the case N\neq 1. So I am wondering what does it looks like, say for N=2 vector multiplet? Another related question is, do we need...

In West's book "Introduction to Strings and Branes", page 2, I don't understand why the auxiliary field e transformed as e'(\tau')d\tau'=e(\tau)d\tau.

I tried to verify that the SYM lagrangian is invariant under SUSY transformation, but it turned out there is a term that doesn't vanish. The SYM lagrangian is: \mathscr{L}_{SYM}=-\frac{1}{4}F^{a\mu\nu}F^a_{\mu\nu}+i\lambda^{\dagger a}\bar{\sigma}^\mu D_\mu \lambda^a+\frac{1}{2}D^a D^a the...

Homework Statement The question asks to find the current I going into the 2k resistor path using Y-delta or delta-Y transformations. Homework Equations Resistance in parallel 1 / R = 1 / R1 + 1 / R2 .. Converting Delta to Y, R1 = RaRb / (Ra + Rb + Rc) Current divider formula Ix = (Rt...

Homework Statement Calculate the result of the transformation of the vector operator \hat{V_{y}} by rotation \hat{R_{x}} around an angle \alpha . Homework Equations I believe that \hat{R_{x}} = \begin{pmatrix} 1& 0& 0\\ 0& cos\alpha & -sin\alpha \\ 0 & sin\alpha & cos\alpha...

Homework Statement Consider the transformation T from ℝ2 to ℝ3 given by, $$T\begin{bmatrix} x_1 \\ x_2 \end{bmatrix} = x_1\begin{bmatrix} 1 \\ 2 \\ 3\end{bmatrix} + x_2\begin{bmatrix} 4 \\ 5 \\ 6\end{bmatrix}$$ Is this transformation linear? If so, find its matrix Homework Equations A...

Hi all, I have an ODE of the form \frac{d^{3}\psi}{d\xi^{3}}-A\left(\psi+\xi\frac{d\psi}{d\xi}\right)=0, where \psi=C_{1}U(\xi)+C_{2}V(\xi). Is there any transformation or inventive manipulation I can use here to obtain an ODE for \sigma=U(\xi)+V(\xi)? As this is the quantity I would...

proof onto Prove: A linear Map T:Rn->Rm is an onto function : The only way I have thought about doing this problem is by proving the contrapositive:

Appendix 1 - simple Lorentz transformation derivation found at - http://www.bartleby.com/173/a1.html Given in equation (3) (x'-ct') = Y(x-ct) [Y = const.] by rearrangement, it yields, (x'-ct')/(x-ct) = Y. But it is stated that both (x-ct) and (x'-ct') are zero, so...

Homework Statement I need to find the laplace transformation of the following function (and it's ok to leave it expressed as an integral). After doing the initial steps and algebra I got Y(s)= g(t)/(s+2)^2 + 7(1/(s+2)^2)+ 2(1/(s+2)^2) the answer is y(t)=2e^-2t +te^-2t...

Problem: A linear transformation T: Rm->Rm is invertible if and only if, for any basis {v1, ...vm} of Rm, {T(v1),...,T(vm)} is also a basis for Rm.Ideas: Since the inverse exists, we can say that some vector u in the inverse of T can be represented as linear combinations of basis vectors...

Hey This is from Numerical analysis course (Legendre polynom) - they gave us the polynomial transformation from [-1,1] to [a,b] as: x = 2/(b-a) * z - (b+a)/(b-a) what is the proof of this tranformation? where did it come from? thanks

Hello, I have few question for deriving the Lorentz transformation (LT): While deriving the LT, we draw a graph as x,y,z in one frame of reference and x',y',z' in the other frame of reference as S and S' as two frames of reference. Now the factor ct comes in, which is the flash of...

Suppose I am in a stationary frame of reference S and there is a lamp post at a distance X from my origin in the positive X direction. Say you move at a velocity V along that axis and the distance of the lamp post in your frame of reference S' is X'. Then by Lorentz transformation equation X'...

Homework Statement Muons are created in the upper atmosphere (at a height of 3000 m) and plummet downward toward a detector at ##v=0.980c##. The mean lifetime of a muon is ##t = 2.20~\mu s##. Find the mean lifetime of a muon measured by an observer on the ground. Find the distance that...

Homework Statement Ok I have a moving person (primed) going 50 m/s in the positive x direction, and I have someone stationary (unprimed) observing them. At t = 0, the moving person is at x(0) = 100m Write an equation for the object’s position as a function of time x(t) seen by the...

Homework Statement Obtain the Laplace transformation of the function defined by f(t) = 0 t<0 = t2e-at t>=0Homework Equations The Attempt at a Solution I'm a little unsure of what I'm doing here, so bear with me. L {t2e-at} = ∫inf0 t2e-at dt = ∫0inf t2e-(a+s)tdt How do I integrate...

I have two questions having to do with the Lorentz transformation for the time...some preamble first: The Lorentz transformation for time along the x-axis is t'=\frac{t-\frac{ux}{c^2}}{\sqrt{1-\frac{u^2}{c^2}}}, where u is the relative velocity of S'. Why is there a dependence on x...

1.what is lorentz transformations ? what are the uses of it ? 2.there are 2 galilean transformations equations .what are the uses of them ? are they useful to find the velocity of the objects at different reference frames or they have anyother applications/uses?

Homework Statement Hi guys, actually this isn't a homework question, but rather part of the working in a textbook on Linear Algebra. Homework Equations The Attempt at a Solution I'm not sure why it's U*li instead of U*il. Shouldn't you flip the order when you do a matrix...

Homework Statement Find Rae, Rbf, Rah, Rcg & Rbc. Homework Equations Am I going to use wye-delta transformation? The Attempt at a Solution I tried checking if I could use wye-delta transformation. There seems to be no parallel connections between the resistors. Please do help...

Hi, I was looking at a basic derivation of the lorentz transformation on youtube. I was wondering at what point do you incorporate the fact that speed of light is same in every reference frame because the guy only uses some algebra on a few equations that come from basic geometry and classical...

Homework Statement Find the Laplace transformation of the following function by using iterations of integration by parts: f(t) = tsin(t) Homework Equations The Attempt at a Solution I know how to do integration by parts (as learned in calculus) but have never seen a funtion...

I'm trying to understand the transformation relations for 2d stress and the book doesn't show the derivation of the 2d stress transformation relations from the directional cosines. The 2d stress transformation relations are found by using the transformation equation and the 2d directional...

Difficulty regarding notation for Lorentz transformation Please can somebody explain to me the relation between Δ^{σ}_{μ} and Δ_{σ}^{μ} as symbols representing a Lorentz transformation? Thanks.

Prove the following {}_2\phi_1 (a,b;c;q,z) =\frac{(b;q)_\infty (az;q)_\infty}{(c;q)_\infty (z;q)_\infty} {}_2\phi_1 \left(\frac{c}{b},z;az;q,b \right)

Homework Statement If T is a linear transformation, proof that Tn is a linear transformation (with nEN). Homework Equations I know that T is a linear application if: T(u+v) = T(u) + T(v) T(au) = aT(u) The Attempt at a Solution Actually I don't know how to start using these two...

May you help me with finding the angle, and what is "line of sight"?(the final answer is 15°) Thank you in advance

What is the difference between orthogonal transformation and linear transformation?