What is Poles: Definition and 240 Discussions

The Poles (Polish: Polacy, pronounced [pɔˈlat͡sɨ]; singular masculine: Polak, singular feminine: Polka), also referred to as the Polish people, are a West Slavic ethnic group and a nation that shares a common history, culture, the Polish language and is identified with the country of Poland in Central Europe.
The population of self-declared Poles in Poland is estimated at 37,394,000 out of an overall population of 38,538,000 (based on the 2011 census), of whom 36,522,000 declared Polish alone. A wide-ranging Polish diaspora (the Polonia) exists throughout Europe, the Americas, and in Australasia. Today, the largest urban concentrations of Poles are within the Warsaw and Silesian metropolitan areas.
Ethnic Poles are considered to be the descendants of the ancient West Slavic Lechites and other tribes that inhabited the Polish territories during the late antiquity period. Poland's recorded history dates back over a thousand years to c. 930–960 AD, when the Western Polans – an influential tribe in the Greater Poland region – united various Lechitic clans under what became the Piast dynasty, thus creating the first Polish state. The subsequent Christianization of Poland by the Catholic Church, in 966 CE, marked Poland's advent to the community of Western Christendom. However, throughout its existence, the Polish state followed a tolerant policy towards minorities resulting in numerous ethnic and religious identities of the Poles, such as Polish Jews.
Poles have made important contributions to the world in every major field of human endeavor, among them Copernicus, Marie Curie, Joseph Conrad, Fryderyk Chopin and Pope John Paul II. Notable Polish émigrés – many of them forced from their homeland by historic vicissitudes – have included physicist Joseph Rotblat, mathematician Stanisław Ulam, pianist Arthur Rubinstein, actresses Helena Modjeska and Pola Negri, military leaders Tadeusz Kościuszko and Casimir Pulaski, U.S. National Security Advisor Zbigniew Brzezinski, politician Rosa Luxemburg, painter Tamara de Lempicka, filmmakers Samuel Goldwyn and the Warner Brothers, cartoonist Max Fleischer, and cosmeticians Helena Rubinstein and Max Factor.

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  1. camilus

    How is the residue computed for a simple pole in the book on prime numbers?

    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...
  2. L

    How do I determine the poles of 1/(z^6 + 1) above the y-axis?

    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...
  3. J

    Can Like Magnetic Poles Theoretically Attract?

    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...
  4. M

    Why Poles move to LOWER Half Plane

    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 +...
  5. V

    Electric machines & power electronics - PMAC machine connected in Y, 4 poles

    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...
  6. G

    Difference of two functions sharing the same poles pole-free?

    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.
  7. M

    Why do poles occur at specific values of q in algebraic function integration?

    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 ...
  8. T

    Cascode C-S Amplifier (Find Poles in Frequency Response)

    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...
  9. E

    Mathematica [Mathematica] How to calculate residues if poles not simple?

    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...
  10. M

    Effect of Poles & Zeros on the bode plot

    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...
  11. B

    Complex Analysis Singularities and Poles

    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...
  12. V

    The Arc length of a cable hanging from two poles x feet apart.

    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...
  13. N

    What happens to magnetic fields when poles are near each other?

    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...
  14. A

    Understanding Z-Plane Poles and Zeros: A Sketching Guide

    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
  15. D

    Contour Integral: how to get the order of those poles?

    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...
  16. P

    Existance of three poles of magnet

    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
  17. R

    A wire exerting force on two poles

    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...
  18. Z

    What happens to the inverse function at infinity?

    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 ??
  19. M

    Designing OHTL Tubular Steel Poles: What Standards Should You Be Aware Of?

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

    Alternating poles in the stator of an alternator

    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...
  21. Borek

    News How to Irritate Poles: A Review of Lies About Jerzy

    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...
  22. M

    Why dont magnets around earth fly towards the earths magnetic poles?

    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...
  23. T

    Poles in the Lippmann-Schwinger Equation

    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...
  24. Z

    Expansion of a function f(x) with poles

    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...
  25. Jonnyb42

    Catenary - rope hanging between poles

    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...
  26. D

    Complex Analysis - Essential Singularities and Poles

    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...
  27. J

    Orders of poles in the complex plane.

    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...
  28. K

    Does a single electron have poles?

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

    Complex analysis- poles vs. Zeros, etc.

    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...
  30. A

    DC Brushless Motor Rotor Steps: 4 Poles North/South?

    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
  31. N

    Solving Simple Poles: Why Does $\frac{e^{ikz}}{z^{2}+m^{2}}$ Have One?

    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 ?
  32. C

    Poles or Removable Singularities

    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...
  33. W

    What is the nature of the singularity at z=0 for the function f(z)=1/cos(z)+1/z?

    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...
  34. H

    Demagnetization of repelling poles

    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...
  35. K

    Why must X(s) occur in conjugate reciprocal pairs for a real x(t)?

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

    North and south celestial poles

    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...
  37. Cyrus

    My Humble Plea: Get Rid of Telephone Poles

    (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...
  38. B

    Understanding poles and zeros of transfer functions

    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...
  39. B

    How Do You Calculate Poles and Zeros of a Digital Filter?

    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...
  40. N

    Complex Analysis: Poles and Singularities

    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...
  41. F

    Probability: random length of poles, how much is lost?

    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...
  42. J

    Magnetic poles (A simple question but I dont know how to answer it?)

    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!?/
  43. J

    How can the force between magnetic poles be accurately calculated?

    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...
  44. A

    Why do the Earth's magnetic poles switch every once in a while?

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

    Residues of Poles in Upper Half Plane for $f(z)$

    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...
  46. U

    Transfer function's poles and Auxiliary Equation

    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...
  47. Y

    If earth's poles are reversed suddenly

    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...
  48. N

    Numerical Integration of Functions with Poles

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

    Integrating Functions with Double Poles: A Contour Integral Approach

    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...
  50. P

    Understanding Simple Poles and Residues in Function 1/(z^4 + 1)

    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...
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