Inversion Definition and 108 Threads

I recently had to solve a problem in which i had to find the inverse laplace transform of some function with a branch cut from - ∞ to 0, so i used a contour avoiding that branch cut like this http://www.solitaryroad.com/c916/ole19.gif my problem is as follows: i know the contributions from...

Hi, I have problem with the calculation the error caused by the lagrange inversion. Hence, accroding to Lagrange theorem if f(w)=z it is possible to find w=g(z) where g(z) is given by a series. I wonder, if I consider up to N-th term in the Lagrange series, what will be the error caused by...

Hi, first time trying to to use the complex inversion formula and I'm confusing myself. I'm trying to find L^-1{ ln(1 + (1/s))} I can see that there is an essential pole at s=0 (is this even right? The power series has an infinite amount of z^n's in the denominator..) and branch points at...

Need help with Weinberg's QFT---Space inversion and time-reversal Weinberg's Quantum Theory of Fields VI. Page 78. He gave the last equation but he didn't prove it, although he qualitatively explained it. I tried to prove it quantitatively but I failed. Also, in page 80, he didn't prove...

I'm inverting this: Y = s2 + 15s + 17 / [(s+1)(s2 + 13s - 4)] I'm using PF expansion, A/(s+1) + Bs + C/(s2 + 13s - 4), I however keep on getting wrong answers, seeing how Runge-Kutta and Taylor approximation disagrees with my final equation. My final equation is...

Hi, I was curious if specific symmetries (or lack thereof) in crystal structure are necessary for the formation of topological insulators. Specifically, do we require that inversion symmetry (or inversion asymmetry) be present in the lattice in order to form the TI state? Thanks, Goalie33

Lens problem! Hi guys, When an object is placed in front of a convex lens ( not between Focus and optical centre ), the image formed on the other side should be inverted and real. My question is, with the mentioned placement of the object, will the image be laterally inverted? Further more...

Hi, Those of you familar with dynamic light scattering (DLS), will know that a common method used to obtain a particle size distribution is via a laplace inversion of the autocorrelation function. What I want to know is why? What does Laplace space have to do with DLS (I've only learned...

Homework Statement Hi, I'm trying to calculate the inverse of a really big matrix (4096x4096) using matlab. The inversion process takes too long on my pc, so i want to find a faster way. The matrix has a strange property that i think could be useful to solve the problem: splitting it in...

Hello everyone, I have enquired about inversion in a sphere here in past: https://www.physicsforums.com/showthread.php?t=440759 Although that time I could not come back to the discussion (apologies to Jason), later I went through some of the properties mentioned by him...

Invesion temp Critical temperature depends on increase or decrease of inversion temp?

Assuming you could put two mirrors (one half-silvered) into the chromosphere, stationary, without them vaporizing/warping..., could they form a resonant chamber and produce laser radiation?

Maybe I am just being stupid, but I don't understand why in the Laplace inversion formula (\mathcal{L}^{-1} F)(t) = \frac{1}{2\pi i} \int_{\sigma-i\infty}^{\sigma+i\infty} e^{st} F(s) ds the contour of integration must be chosen so that \sigma is greater than the real part of all...

Homework Statement Given the unit circle (in the Euclidean plane) centered at the origin x^2+y^2=1, and a general circle D with equation (x-a)^2+(y-b)^2=c^2 that does not pass through the origin (ie the center of inversion, ie a^2+b^2≠c^2, prove analytically that the inversion of D in the...

Homework Statement Find an inversion of the following cycle (143) Homework Equations (143)^{-1} The Attempt at a Solution Could someone show me how do we compute this?

Homework Statement Show that the inversion mapping w = f(z) = 1/z maps the circle |z - 1| = 1 onto the vertical line x = 1/2. Homework Equations The Attempt at a Solution z = a + ib w = x + yi = a^2/(a^2 + b^2) + ib^2/(a^2 + b^2) |z - 1| = |(a -1) + ib | = 1 (a - 1)^2 + b^2 = 1...

Hello! I'm reading up on Hamiltonian mechanics and i stumbled on the fact that the curl of the vector potential can be expressed as B_k = \sum_k \epsilon_{kij}\frac{\partial A_i}{\partial x_j} Now the text that I'm reading says that this formula can be inverted as \sum_k \epsilon_{kij}...

Help with Mobius Inversion in "Riemann's Zeta Function" by Edwards (J to Prime Pi) Can someone please add more detail or give references to help explain the lines of math in "Riemann's Zeta Function" by Edwards. At the bottom of page 34 where it says "Very simply this inversion is effected...

I encountered this beautiful theorem and then I tried hard to prove it using ordinary algebraic methods and my understanding of calculus without involving real analysis in it but I didn't succeed. The theorem states that if f is an analytical function at some point x=a then f-1 has the following...

Hello guys, I'm writing a C++ function for matrix inversion. I saw many algorithms online, but I'm concerned about the case when a diagonal element equals zero, which is, for some reason, not taken into account by those websites. When we do the elimination for solving a system of linear...

Hello, I'm trying to find a fast way to solve the matrix equation (A+pI)x=b, where A is a large matrix, I is the identity matrix, and p is a parameter whose value needs to be swept. Obviously I could just use mldivide or matrix inversion for every value of p, but this seems inefficient. Does...

Hey guys, I tried to figure this out and got a rough estimate but thought I’d ask the experts. I use the Sola SDU500 UPSs in our systems. A customer wants to know how long they will last if there is a power outage. I believe the power consumption for the entire system would be ~12Wh...

How is this accomplished? How can one derive equations for stress in terms of strain from equations of strain in terms of stress or vice versa?

Would like to show \sum_{d \mid n} \mu (d) \sigma_0 (d) = (-1)^{\omega (d)}. This proof is just left out of text I'm looking at and I can't seem to piece how F(n/d) = \sigma_0 (d), where F(x) = \sum_{s \mid x} f(x).

Hi, I am a bit confused about the MOS strong inversion case. When Vg>>Vth, is the equation describing gate voltage at threshold still applicable? If not, what is the expression for corresponding surface potential and depletion width. Some books suggest that surface potential and depletion...

Hello to everyone! I need to invert the following infinite continued fraction: 0=\beta_{0}-\frac{\alpha_{0}\gamma_{1}}{\beta_{1}-}\frac{\alpha_{1}\gamma_{2}}{\beta_{2}-}\ldots, n=1..\infty to something starting with the \beta_{n} term and going down to n=1 (where n is the term the fractions...

Hello, I need to invert a non-square matrix A under the constraint that the absolute value of each component of the solution is less than some maximum. In other words, I want \vec{b} such that A . \vec b = \vec c and |b_i| < \alpha. Are there any established methods for doing this? My...

let be m a measures (by expermients) physical quantity and m0 a 'bare' value of these physical quantity , let us suppose that we can expand m= m_{0}+f(k,m_{0})+ \sum_{n} u^{n}c_{n} for some finite quantities c_n and u=log(\Lambda) with lambda a regulator can we then invert the...

Homework Statement 1) Given a circle, construct another circle which is orthogonal to it. List the steps taken in this construction. 2) For a fixed circle and a point P not on the circle nor equal to the center of the circle, construct the image of P under inversion with respect to the...

I need to deduce that \hat{\hat{f}}(x)=2\pif(-x) using the inversion formula for the Fourier transform, I was wondering if someone could explain why there's f(-x) because i just can't get started on this problem!

Homework Statement Let A be a 2x3 matrix with real coefficients, and suppose that neither of the two rows of A is a scalar multiple of the other. By quoting an appropriate theorem from linear algebra, show that for some j \in {1,2,3}, the 2x2 matrix obtained by omitting the jth column of A is...

Can somebody give me an example whereby I use the inversion with respect to a circle (unit circle or otherwise) and the problem becomes easier. I guess I am asking: how do I make use of this notion. Or a problem that involves inversion, period. Thank you

How do you get a vector to the power of negative one? I.E. : V ^ (-1)? Or inversion if that's what it's called? Thank you.

Hi, I'm just reading about the group SL(2,C). In the book that I'm using(Jones, groups reps and physics), he defines a 2x2 matrix from a generic 4 vector v_{\mu} and a vector \sigma_{\mu}:=(1,\vec{\sigma}), as V:=v_{\mu}\sigma^{\mu} He nows wants to invert this equation to solve for...

Hi, I think i should have posted here instead of where I posted before. I don't know how I missed the homework help section... anyway Well, I'm required to solve this heat transfer problem. T1 is 25c and q'' is 100w/m2 Ok, so I can get it to do it in 1 dimension and my numbers...

When trying to solve a pde using Laplace transform, I need to invert an expression of the form \frac{\exp{(-as-b\sqrt{s})}}{s^2} A friend told me that Mathematica cannot invert such expression. I try using convolution but a bit loss when trying to evaluate the integral of Erfc(.)...

I was trying to expand a three and more parameter functions similarly to the two-parameter case f(x,y)=(f(x,y)+f(y,x))/2+(f(x,y)-f(y,x))/2. Anyway, to do the same for more parameters I need to solve \begin{pmatrix} 1 & 1 & 1 & \dotsb & 1\\ 1 & \omega & \omega^2 & \dotsb & \omega^{n-1}\\ 1 &...

Hello everyone! I need to find the vector x in the problem A.x = b I have matrix A and vector b. Inverting the matrix would do it, but in my case, the matrix is quite big. Luckily, it is extremelly sparse (lots of 0), so I guess there could be some way to take advantage of it. The best...

the idea is let us suppose i must solve f(x)= 0 (1) let us suppose that f(x) have SEVERAL (perhaps infinite ) inverses, that is there is a finite or infinite solutions to the equation f(x)= y by g(y)= x with f^{-1}(x)=g(x) then solution to equation (1) would be g(0)=x...

Hi, I want to inverse this laplace transform, -(s^(1/2)), seems that the inverse is in complex plane. Where should i start to find this inverse... Thank you.

we keep a clock in front of the mirror,if lateral inversion occurs,what will happen?

What is the mean of " Effective logic inversion " ? Because I can't understand this qustion, " Describe briefly why there is an Effective logic inversion between logic level from a TTL IC and the LED load it drives? "

Anyone have opinions on teeter hang ups? Below is what they claim: http://www.teetertv.com/

Hello, I bought a Meade NGC-70TC refractor telescope and the image is inverted left-to-right. Is that normal? A google search didn't yield any answers.

Hi, I'm trying to prove that X=(X_{t})_{t\geq0} is a Brownian Motion, where X_{t} = tB_{1/t} for t\neq0 and X_{0} = 0. I don't want to use the fact that it's a Gaussian process. So far I am stuck in proving: \[ X_{t}-X_{s}=X_{t-s} \quad \forall \quad 0\leq s<t \] Anyone has any ideas?

The parts of this problem form a proof of the fact that if G is a finite subgroup of F^*, where F is a field (even if F is infinite), then G cyclic. Assume |G|=n. (a) If d divides n, show x^d-1 divides x^n-1 in F[x], and explain why x^d-1 has d distinct roots in G. (b) For any k let \psi(k)...

Homework Statement Suppose A is an invertible mxm matrix, B is an invertible nxn matrix, and C is an arbitrary mxn matrix. Is the matrix M = A|C ---- O|B invertible? Solve with proof. Hint: Use block multiplication. Note: I'm not quite sure how to draw this matrix on the forums. It...

What is the criteria to know whether a function may be inverted into an elementary functional form?

[SOLVED] inversion layer in a MOS Hello, I have some questions about MOS devices, and CCD In a MOS or MIS after applying a voltage on the metal, the valenceband and the conduction band bend downwards (in the usual band diagram) when a positive voltage is applied. (p-type semiconductor)...

But..is really so easy? (Möbius inversion), let be F(x) and G(x) functions F(x)= G(ax)+G(2ax)+G(3ax)+... for n=,1,2,3,4,5,... a is a fixed real number. then G(ax)= \sum_{n=1}^{\infty}\mu (x) F(nx) is seems too easy for me, to be true.