Example Definition and 879 Threads

I wonder how and where does resonance is applied in our real life. Any example?

Second thread on the evolution of like, in the Archaen and Proterozoic eons. There are many kinds of eyes, and many have arisen quite independently; the classic example of convergent evolution. Did sexual reproduction arise more than once, independently? Is it too an example of convergent...

I'm reading a QFT text right now and to fully understand the physical perturbation theory method I would like anyone to suggest a refrence or supply an example of a calculation using the physical perturbation theory: As an example to start a discussion consider. L = \frac{1}{2}((\partial...

I still don't understand circular reasoning. Can you guys give me some example? From Physics section:"Wave is something satisfying wave equations". I don't know why this sentence is "circular". Thanks:smile::cool::wink:

Can you give an example of a function f:X\times Y\to\mathbb{R}, where X,Y\subset\mathbb{R}, such that the integral \int\limits_Y f(x,y) dy converges for all x\in X, the partial derivative \partial_x f(x,y) exists for all (x,y)\in X\times Y, and the integral \int\limits_Y \partial_x...

The latex code here is doing all sorts of odd things... :( ... anyway, The convolution algebra is l_1(\mathbb{Z},\mathbb{C}), the set of functions f:\mathbb{Z}\rightarrow\mathbb{C} which satisfy ||f||:=\sum_{n=-\infty}^{\infty}|f(n)|<\infty with pointwise addition and scalar...

Can anyone give an example of a ring homomorphism f : R -> R', such that R is a integral domain but the Image(f) is not an integral domain. I was thinking that since we want two non zero elements of Image(f) multiply to 0, we require: f(xy) = f(x)f(y) = 0, with f(x), f(y) not 0. Now f(xy) =...

is it possible for a body to rotate on its centre of gravity

In quantum field theory of high energy physics one encounters so called anomalies like e.g. of the kind discussed in this thread: https://www.physicsforums.com/showthread.php?t=406540 As far as I understood, it basicallymeans that the classical theory has a higher symmetry than the qft. Does...

Homework Statement My book gives the theorem for parabolas as: The graph of the equation: y = ax^{2} (where a \neq 0 ) is the parabola with focus F(0,\frac{1}{4}a) and the directrix y = -(\frac{1}{4}a). Its vertex is (0,0) , and its axis is the y-axis. It then goes on to...

I was trying to be more clear on how this equation works. I appreciate any help.

Can you give me a "least squares" example? Assume that, I have a function to estimate like below: f(x) = a3x3 + a2x2 + a1x1 + a0x0 After several experiments I have obtained these (x, f(x)) pairs: (x1, y1) (x2, y2) (x3, y3) (x4, y4) (x5, y5) (x6, y6) How can I estimate a0, a1, a2...

This needed a separate thread. Here is an APL example where it's all done with no interation using N by N matrices in the intermediate propagation of data. Note, code flow in APL statements is right to left. The []IO<-0 sets the "index origin" to zero so a list of numbers and indexing...

Hi Guy's I need to show that two spaces are Homeomorphic for a given function between them. Is there an online example of a proof. A lot of text on the web tells you what it needs to be a homeomorphism but I not an example of a proof. I just want an good example I can you to help me...

Homework Statement Give an example of two norms on a vector space that are not equivalent. Homework Equations The Attempt at a Solution Hi everyone, I know the definition for equivalent norms. I also know that norms on a finite dimensional vector space are equivalent. So...

Homework Statement From pages 124-125 in edition 3. This is about the restricted three body problem (m3 << m1,m2) http://img718.imageshack.us/img718/7012/3bdy.jpg Homework Equations L = T-V Euler-Lagrange equations The Attempt at a Solution I'm interested in m3, the...

The problem at hand: \inline{\sum_{k=1}^n \frac{(k+1)!}{(k+3)!}} Hence, find the limiting sum of the series, as n ---> infinity. Start this summation by expanding out the factorial to have a common factor of k!(k+1) as follows: \sum_{k=1}^n \frac{(k+1)!}{(k+3)!} = \sum_{k=1}^n...

Im working on some problem for a chemical thermodynamics course, and I've solved a question (maybe incorrectly) which is making me question my understanding of entropy. Basically, the system in question is a turbine, with one stream in and one stream out. The turbine is insulated, hence no...

Homework Statement Consider the series \frac{1}{2} + \frac{1}{3} + \frac{1}{2^2} + \frac{1}{3^2} + \frac{1}{2^3} + \frac{1}{3^3} + \ldots. He then proceeds to write \lim \textnormal{inf}_{n\to\infty} \frac{a_{n+1}}{a_n} = \lim_{n\to\infty} \left(\frac{2}{3}\right)^n = 0 and...

Verify the divergence theorem when F=xi+yj+zk and sigma is the closed surface bounded by the cylindrical surface x^2+y^2=1 and the planes z=0, z=1. I've done the triple integral side of the equation and got 3pi but don't know how to solve the flux side of the equation \oint\ointF.ds. Any...

http://wadvpress.org/?p=58 http://docs.dads-house.org/Statutory_Rape_Victims_Must_Pay_Child_Support.pdf Only in America could a guy get raped and have to pay the child support too.

Is it possible to map the unit disk onto the complex plane C holomorphically? This is not a homework question. Thank you for your help

I just need a simple example, preferably one to do with voltage. thanks for any help :)

Imagine a metal hoop floating in a plane parallel to the Earth's surface, with a permanent magnet suspended above it. The magnet is then dropped straight through the center of the hoop. From Faraday's Law, a current is induced in the hoop as the magnet passes through. There is now angular...

Homework Statement This is am example from my textbook \int_{1}^{3} x^2 dx = 26/3 It then goes to define the arbitrary partition in [1,3] and maximum / minimum for each subinterval blah blah.. then it says For each index i, 1 <= i <= n, 3x_{i-1}^2 \leq x_{i-1}^2 + x_{i-1}x_i + x_i^2...

when I first learned about homeomorphic sets, I was given the example of a doughnut and a coffee cup as being homeomorphic since they could be continuously deformed into each other. fair enough. Recently I heard another such example being given about diffeomorphisms: "Take a rubber cube...

Hey, I'm new here, so I hope this hasn't already been posted, but I really need help with this question. There is a commonly used example to show how Einstein helped prove General Relativity through space curving due to different ratios in radians of a spinning wheel made to spin at the velocity...

Can someone provide me an example of three sets of integers A, B and C such that A\cupB=A\cupC, but B≠C. And also, A\capB=A\capC, but B≠C. Thanks a lot :)

Please explain me the toppling giving example of a block on horizontal surface? Is friction necessary? What's its deal with center of gravity?

This should be very simple, but I can find a simple example that violates my general conclusion. I clearly must be doing something wrong with my integration by parts. Any suggestions would be great. Define a distribution such that the density; \eta(\vec{x})=\int d\vec{k} f(\vec{x},\vec{k})...

Can somebody give an example of two matrices a_1 and a_2 which would satisfy the relation a_i a_j^{\dagger} + a_j^{\dagger} a_i = \delta_{ij} I know that \left(\begin{array}{cc} 0 & 1 \\ 0 & 0 \\ \end{array}\right) \left(\begin{array}{cc} 0 & 0 \\ 1 & 0 \\ \end{array}\right)...

The train example discussing non-simultaneity that I'm sure most of you have heard of: However, wouldn't the passenger see the strikes of lightning at the same time? As she is in an inertial reference frame and is equi-distance from the front and back?

"If a random variable has a probability density function, then the characteristic function is its Fourier transform" - http://en.wikipedia.org/wiki/Characteristic_function_(probability_theory)#Definition". I have never come across a random variable that did not have a probability density...

This is not homework, per se, but I have recently started reading Courant and Robbins' What is Mathematics? Homework Statement Prove by mathematical induction. (1+q)(1+q2)(1+q4) ... (1+q2n) = (1-q2n+1) / (1-q) Homework Equations Only the problem itself.The Attempt at a Solution Using the...

This is my first time posting so it's nice to meet everyone! I'm not trained in physics, but lately I've been very interested in and reading a lot about both Relativity and Quantum Mechanics. With regard to relativity, I found the topic of relativity of simultaneity very interesting. The...

I've found what looks like a really easy problem. If I can be clear about this one, I'll probably start to get somewhere with some of the more difficult ones. So I'd really appreciate it if someone could point out any mistakes/missunderstandings in my attempt at the answer; I'd like to nail...

Does anyone have a graphic example of beat vibration?

Hi All, If I is an ideal of J and J is an ideal of R (the ring)... Is it possible that I is not an ideal of R. When are we guaranteed to have this transitivity, if at all? Thank you

I'm not very experienced on heat laws and devices, other than general thermodynamics. But I am studying 2nd order systems, and the curiosity came up if there is a 2nd order thermo system, since my book only described a 1st order one. I see the thermal capacity as an electronics capacitor...

My current understanding of the Riesz representation theorem is that it is useful since it tells you what all bounded linear functionals on Lp look like. They look like the integral of fg where g is some function in Lq. So, I was trying to think of an example of a bounded linear functional on an...

in my book it asks me to give an example of a linear transformation T: p4 -> R^4 that's onto. I have to prove that T is onto and a linear transformation...can someone give me some advice?

Homework Statement 3 unit masses move around a unit circle. Between them there is a repulsive force that decreases with the angle between the particles as F_{ij}=\exp(-(\theta_i-\theta_j)) The problem is to find 3 conserved quantities in involution. Homework Equations The...

An example of a function that attains the value "infinity" on R? I'm reading a couple of books on introductory measure theory (Royden, Stein-Shakarchi), and both of them talk about functions that can possibly attain the value \infty. But they don't define exactly what this means, or give...

Homework Statement Give an example of a subspace W of a vector space V such that there are two projections on W along two distinct subspaces. Homework Equations The Attempt at a Solution I tried looking into Euclidean geometry spaces (R3 and R2) but no matter what subspace W I...

Homework Statement hello this is a example problem in book "Probability, Random Variables and Stochastic Processes 4th ed - Papoulis" pg 183 i am wondering how particular value came.i havemarked with red circle it in attached pdf file. please take a look thanks Homework Equations...

Homework Statement Give an example of a function f(x) that is discontinuous at each point of its domain, whereas f(f(x)) is continuous everywhere. Homework Equations The Attempt at a Solution I guess the function has to be defined piecewise, but I don't know how to approach this...

Can someone give me an example where we have \mathbb{E}z=0 , \mathbb{E}z^2=1 (i.e. finite expectations) BUT, \mathbb{E}z^4= \infty ? Also, I cannot think of a case where: \mathbb{E}x=\infty where x>0 BUT, \mathbb{E}| \log x |< \infty Thanks in advance

Homework Statement From Young and Freedman's book University Physics, ch 23, problem 23.54: In the Bohr model of the hydrogen atom, a single electron revolves around a single proton in a circle of radius r. Assume the proton remains at rest. ++ (the rest is irrelevant to my question)...

Hello, I apologize in advance for what is probably a boneheaded question, but I'm just a little bit confused. I just started reading The Elegant Universe and in the chapter on the theory of relativity, the author uses an example of a photon-based clock to illustrate how the perception of...

Homework Statement We'll show that, if x => -1, then (1 + x)^n => 1 + nx for all positive integers n. Solution ... The text goes on to explain that if n = 1 is true, we assume n = k is true, and n = k + 1 is true. I understand everything until this part: Since (1 + x)^k+1 = (1...