Poles Definition and 240 Threads

my book on prime numbers has a line where it skims over a residue computation, and I am in dire need of clarification. It's rather simple, and I may very well be the one mistaken, but I am getting a extra factor of 1/2 in the residue whereas in the book it does not appear and apparently isn't a...

Kind of stuck (embarrassingly) on determining what poles of the function: 1/(z^6 + 1) lie above the y-axis (I'm solving a contour integral using the residues theorem). What's the easiest way to do this? Normally I'd write z as e^(theta + 2kpi)/6 , where theta is the angle that -1 forms...

Not meant to be a homework question, but since I don't have any valid data on hands so I am hesitate posting this in classical physics forum. The headline suggests the opposite of what we physics tell us. But my question is, is it theoretically possible to make like poles attract (assuming no...

Pretty simple question here guys, but I can't get my head around it. When solving say, the Greens Function for the driven harmonic oscillator, one needs to use the Residue method of integration. So, one adds a complex quantity to your variable w (angular frequency), so we now have w ---> w +...

Homework Statement A PMAC machine is connected in Y and has 4 poles. I_F\,=\,27\,A and L_m\,=\,20\,mH. a) It is to operate at a torque of 35 Nm and at a speed of 4000 RPM. Calculate the necessary stator current I_S and voltage V_{S\,line-to-line} so that the losses are minimal. b) If the...

If f(z) and g(z) share all the same poles, is f(z)-g(z) pole-free? I feel like this would be true, but I can't really come up with a proof for it.

Say I am integrating some algebraic function with respect to a variable q. There is also an exp( iq ) in the integral as a factor. There are poles when q takes a certian value as it is in the denominator as q - A, so pole at q = A.I know the poles are in the upper left plane, and lower right ...

Homework Statement Heres the question, I honestly don't know where to even begin :( An AC model of a cascode common-source amplifier is shown below. M1 and M2 are biased in saturation mode. The parasitic capacitors in the transistors are included. Determine the poles in frequency response...

Hey guys, i have the following situation: I have a function which looks like \frac{(a+bx)^3}{(x-y)^6(x-z)^6} As one can easily see this function has poles at y and z of order 6. Now, I know how to calculate the residue of this function for instance at y, but how do I implement this into...

Homework Statement What are the effects of poles and zeros of a transfer function on its magnitude graph. Note: The Transfer function is discrete. Homework Equations zeros= roots of numerator poles=roots of denominator The Attempt at a Solution I really don't have any idea. I...

Assume throughout that f is analytic, with a zero of order 42 at z=0. (a)What kind of zero does f' have at z=0? Why? (b)What kind of singularity does 1/f have at z=0? Why? (c)What kind of singularity does f'/f have at z=0? Why? for (a) I'm pretty sure it is a zero of order 41...

Homework Statement I appologize if this is in the wrong topic. But, I need help with the. I know you guys don't exactly give out the answer, but I'm looking for a particular rule of something that will help me. My calculus professor told me to use any available resource to solve this problem...

What happens when same magnetic poles (i.e., NN or SS) are next to each other for say an hour or more - will the magnetic fields of those magnets become weaker or stronger? What happens when different magnetic poles (i.e., NS or SN) are next to each other for say an hour or more - will the...

I have been asked to sketch the Z planes poles and zeros for the follwoing: H(z) = ((z-1)^2 (z+1)^2) /(z-0.7)(z+0.9+0.95j)(z+0.9-0.95j) I have the denominator points sorted. Would the numerator points be: (z-1)^2 =0 z-1 =0 z=1 and (z+1)^2 = 0 z+1 = 0 z = -1

Homework Statement The following function : a) f(z) = \frac{1}{z^6 + 1} has simple poles on : z_1 = e^{pi/6 i}, z_2 = e^{3pi/6 i}, z_3 = e^{5pi/6 i} I know how to get the poles, but how could I demonstrate they are simple (order 1) ? I tried to write the Laurent series...

I consider two magnets of smae pole strength and length. If i bring either of similar poles of the magnet forcefully near and stick with a glue. Is the combination a magnet with three poles? Thank you for your help

Homework Statement A wire, weighing 10N, is put on two poles that are 40m apart. Due to its weight, the wire dips for 1m. What are the forces the wire exerts on each of the poles? The wire can be said to take a shape of an arc of a circle.Homework Equations The Attempt at a Solution Well, the...

let be a function y=f(x) with poles f(a_{i} ) = \infty for some real 'a' my question is if we define the inverse function g(x) so g(f(x))=x ,then is this true g(\infty)=a_{i} my question is that it seems that g(x) would have several asymptotes as x-->oo how it can be ??

Does anybody knows a standard way of determining the hight of 11 KV transmission line galvanised steel poles ?

I have run into something i don't understand while working with an alternator. I purchased a magnetic pole detector to identify the poles of some magnets and tried to see if i could detect the changing magnetic field of the alternator in my car while it was running by placing the pole detector...

http://latimesblogs.latimes.com/culturemonster/2010/06/theater-review-more-lies-about-jerzy-at-the-hayworth-theatre.html Probably this is just a sign of stupidity, or arrogance, or both. But "Nazi Poland" is about as correct as "Polish concentration camps". Yes, it happened in Poland, but is...

Why don't magnets fly to Earth's magnetic poles? I understand that Earth's magnetic pull must be strong enough to pull a magnet to the pole, but what is the force required for a magnet to get pulled the over their? How does one calculate whether a magnetic field is strong enough in order for two...

While deriving the Helmholtz Green function in Sakurai we come across the integral \int_{-\infty}^{\infty}q\,dq\,\frac{e^{iq|\vec x-\vec x'|}-e^{-iq|\vec x-\vec x'|}}{q^2-k^2\mp i\varepsilon'} This equation has poles at q \simeq \pm k\pm i\varepsilon', however when doing the residue calculation...

If a function f(x) have SIMPLE POLES , could in principle this f(x) be expanded into f(x)= \sum_{r}a_{r} (x-r)^{-1} where 'r' are the poles on the complex plane of the function Another question, would it be possible to relate using the Euler-Mac Laurin resummation, a series of the...

Homework Statement Problem is regarding approximating the value of a in y= a cosh(x/a) using Newton's method, and then use a to find the length of the rope. That equation represents the curve formed by a rope hanging with it's ends attached to poles at a distance 2b. (cosh() = hyperbolic...

Homework Statement Find two analytic functions f and g with common essential singularity at z=0, but the product function f(z)g(z) has a pole of order 5 at z=0. Homework Equations Not an equation per say, but I'm thinking of the desired functions in terms of their respective Laurent...

Homework Statement For a function f(z)= [e^(2*pi*i*a*z)] / [1 + z^2] I need to find the order of the poles at i and -i. (I'm pretty sure these are the only poles.) Homework Equations The Attempt at a Solution I'm not totally clear on how I go about finding the orders. I have a...

If so, why? Shouldn't it attract positive charges equally from all sides?

I am having a hard time understanding the difference between poles and zeros, and simple poles versus removable poles. For instance, consider f(z)=\frac{z^2}{sin(z)} . we can expand sine into a power series and pull out a z, so doesn't that remove the singularity at z=0? Also, I don't see why...

Hello Forum, I have a 3 phases DC brushless motor from a Hard Disk Drive, when energize one coil and turning by hand the rotor i can feel 4 steps per rotation, is this means that this motor has 4 poles of north and south? Thank you in advance, Anita

In the mathematical text I've read, it says that \frac{e^{ikz}}{z^{2}+m^{2}} has only one simple pole, that is, im, if k>0 . Why? Has it got 2 simple poles, I am and -im ?

Homework Statement Determine the location and nature of singularities in the finite z plane of the follow function and apply Cauchy Integral Formula Homework Equations g(z) = sin 2z ------- z^15 The Attempt at a Solution I know there is a pole of order 14 at z = o...

Homework Statement Determine the nature of the singularity at z=0Homework Equations f(z)=\frac{1}{cos(z)}+\frac{1}{z} The Attempt at a Solution by expanding into series: f(z)=\Sigma_{n=0}^{\infty} \frac{(2n)! (-1)^n}{x^{2n}} + \Sigma_{n=0}^{\infty} (-1)^n (z-1)^n Now \frac{1}{z} has no...

Bit of a simple question but one I've never really had to think about. Lets say you have two opposing poles of a magnet (a ferromagnet i guess), they repel of course, but will forcing them to stay next to each other eventually demagnetize them? My instinct tells me no, but maybe the force...

Hello, if i said that x(t) is real, why X(s) must occur in conjugate reciprocal pairs ?

Homework Statement The Earth's angular momentum is directed toward which celestial pole(north or south)? Homework Equations none The Attempt at a Solution I just assume that it is the south celestial pole considering that the Earth is spinning from left to right, or west to east...

(a) Telephone Poles. I really, really hate telephone poles. They are abhorrently ugly. Every time I drive down the road- wires, wires, wires. Everywhere wires! I live way too close to a major city for there to be wires everywhere. The water is under the ground in pipes, why does the power...

Hello again, as I was reading today still trying to grok passive filter design, I realized that I do not entirely grasp the concept of "poles" and "zeros" from in a qualitative way. I understand, for example, that a pole is a kind of singularity where the denominator of the complex-number...

1. Given equation: y(n) = x(n) + x(n - 2) - 0.81y(n-2) a) Find the poles and zeros b) Determine its z transfer function 2. Z transfer: H(z) = (SUMOF(a(m)*z(^-m))) / (1 - SUMOF (b(m)*z (^-m))) [b]3. I get the feeling that this is pretty easy, I just don't know the required...

Homework Statement Hi all. According to my book, a pole z_0 of a function f(z) is defined as \mathop {\lim }\limits_{z \to z_0 } f(z) = \infty. Now let's look at e.g. f(z) = exp(z). Thus we have a singularity for z = infinity, since the limit in this case is infinity. This is what I don't...

Suppose the length of a pole is a random variable X, with mean m(x) and probability density function f(x). Poles are cut to obtain an exact length L. If the initial length of the pole is less than L, the entire pole is lost. If it is greater than L, the pole with be cut down to L, and the...

Magnetic poles (A simple question but I don't know how to answer it?) (i)Show the magnetic field associated with the earth, (ii)and use your diagram to explain why magnetic poles always occur in north south pairs I don't know how to go about the second part at all!?/

Hi, I was wondering if anyone could tell me how to calculate the attractive force between a pair of magnets. I orignally thought that this would involve a really simple formula (something of the 1 over r squared variety) but have struggled to find any equations dealling with the force between...

My geology prof says that no one knows. I think I'll cry if that's true. It's driving me nuts.

for the function f(z)=\frac{ze^{iz}}{z^4+\alpha^4}, \alpha>0 what are the residues of the poles in the upper half plane so i factorised the denominator to (z^2+i \alpha^2)(z^2-i \alpha^2) my problems are: (i)but then i wasn't sure how to characterise this the z^2 had me confused as to...

Why does the homogeneous of a second order differential equation/system (i.e. a series RLC circuit) is identical to the transfer function (i.e. H(jw)) denominator in its standard form? Therefore the poles of the transfer function are also the solutions for the auxiliary equation... I cannot...

Homework Statement Consider the Earth’s magnetic field as that of a dipole with the magnetic field around the equator having magnitude 30 µT. The radius of the Earth is 6.37 106 m. a. Calculate the magnetic flux φB in low Earth orbit (r=6.5x10^6 m) at the equator, in units of Tm2. b...

What are some simple techniques to numerically integrate functions with poles?

Hi, Can someone tell me how to integrate functions which have a branch point and a pole (of order > 1) on the x-axis. Specifically, I ran into the following problem while playing around with contour integrals, which has a double pole at x = -2 . I tried to do this with a keyhole contour...

I have a function 1/(z^4 + 1) I know the poles are pi/4, 3pi/4, 5pi/4, 7pi/4 It says they are simple poles, I thought I understood why, but now I am totally confused. How does my lecturer just know that they are simple? A simple pole is a pole of order 1, but I thought this meant you...