Example Definition and 845 Threads

In section 1.2 of Taylor and Wheeler's Spacetime Physics, a rocket moves past a laboratory (on Earth). Attached to the rocket is a pin. From that pin a spark is emitted at two locations in the lab, separated by 2 meters. The observer in the rocket measures the elapsed time between the sparks, as...

A disk, cylinder shaped, of mass m and radius r is initially motionless on an ice rink. It has a massless string wound around it which you pull with a constant force F. After your hand has moved a distance d. How far has the c.m. of the disk moved? If someone could show me how I could do this...

Homework Statement Hey I am confussed about how the Fourier trick works. In my book they have an example ...=integral from 0 to pie Pl(cos@)Pl'(cos@)sin(@) d@ then somehow they get ={0 if l' does not equal l and 2/2l+1 if l'=l Thanks Homework Equations The Attempt at a...

Very early on in Feynman's Lectures on Physics, he offers the example of a screwjack with a mass on it to demonstrate the conservation of energy (picture attached). He asks how much force would be needed to lift the one ton sitting on top of the screwjack. He then comes up with 1.6 pounds...

Homework Statement let X be the set of all infinite dimensional vectors with finite nonzero components consider 2 distance functions on X d=euclidean distance=\sqrt{\sum(Xi-Yi)^{2}r=max distance=max{|X1-Y1|, |X2-Y2|, ...} give an example of a sequence where it converges under r but not...

The acid: Hydrochloric What happens step by step? I am unfamiliar with acids and bases, so I just want to know what's happening to help figure out. Thanks.

Hi, Everyone: A question on knots, please; comments,references appreciated. The main points of confusion are noted with a ***: 1)I am trying to understand how to describe the knot group Pi_1(S^3-K) as a handlebody ( this is not the Wirtinger presentation; this is from some...

Homework Statement Prove that for a linear set M a subset of Hilbert space, that the set perpendicular to the set perpendicular to M is equal to M iff M is closed. The Attempt at a Solution I already have my proof -- but what is an example of a linear subset of H that is not closed? I think...

Hello, this could be a basic question. I saw the link http://www.drchinese.com/David/Bell_Theorem_Easy_Math.htm" on one of the threads. Following the table there the probability of complete match between two detectors happens twice out of 8 times. i.e. 1/4. How how can we say that it...

Hi guys In my statistics book there is an example. They say that we see 3 occurrences of type A, and theoretically expect 7. This is a difference of 4, since we know that the standard deviation is 1.65 (they calculate it), then the difference is 2.4 standard deviations. Looking at a table of...

Suppose that S=[0,1)U(1,2) a) What is the set of interior points of S? I thought it was (0,2) b) Given that U is the set of interior points of S, evaluate U closure. I thought that U closure=[0,2] c) Give an example of a set S of real numbers such that if U is the set of...

Homework Statement I am following along in an example problem and I am getting hung up on a step. We are seeking a power series solution of the DE: (x - 1)y'' + y' +2(x - 1)y = 0 \qquad(1) With the initial values y(4) = 5 \text{ and }y'(4) = 0. We seek the solution in the form y(x) =...

Homework Statement X and Y are two closed non-empty subsets of R (real numbers). define X+Y to be (x+y | x belongs to X and y belongs to Y) give an example where X+Y is not closed Homework Equations The Attempt at a Solution i tried X=all integers and Y=[0 1] but that didnt work out. i know...

Hello everyone. I was going through my Linear Algebra Done Right textbook that threw me off. I hope this forum is appropriate for my inquiry; while there is no problem I'm trying to solve here, I don't know whether just asking for clarification would belong to the homework forum instead. If...

Example of a "pure existence metaproof" http://en.wikipedia.org/wiki/Existence_theorem A pure existence theorem is a theorem which states the existence of something, but the proof of the theorem does not indicate a construction of the thing in question. As the article mentions, this is...

Hi. I am having a bit of trouble working through all the formulas for calculating the total composite mass of moving particles. If I could just fill in this 'black and white' and very intuitive example then I will be able to use it as a guide to test everything I'm doing. If we have 2...

Hi, I am trying to find a worked example of the k.p. method for a semiconductor. I understand the theory, but would like to find an example of its implimentation for a simple system just to help with my understanding of it. Many thanks in advance

Take the discreet metric on an infinite set A. I understand that its closed (because it contains all of its limit points), but I don't understand why its bounded and why its not compact. Also, when they say "an infinite set A" do they mean a set that extends to infinite (say, [1,n] for...

Homework Statement Give an example of a nonempty set A in R such that A = Bd(A) = Lim(A) = Cl(A). Bd(A) is the boundary of A, Lim(A) is the set of limit points of A, Cl(A) is the closure of A. Homework Equations Bd(A) = A - Int(A), Int(A) is the interior of A Lim(A) = is the set of...

Hi, I've a question that I'll illustrate by presenting the following example: Let's imagine Einstein in a car that's moving away from a clock. This clock 'send' a light beam with the information 'It's 12 o'clock'. If the velocity of this car is close to c, I understand that Einstein will...

Non-convergence counter example?? (This question occurred to me in the context of quantum field theory, but since it's purely mathematical, I'm asking it here...) Consider the universal vector space \Xi of arbitrary-length sequences over C (the complex numbers). Denote \delta_k ~:=~...

Consider the manifold of the real-line R with a differentiable structure generated by the map x^3 : M \rightarrow \mathbb{R} . This example is given in a textbook I'm looking at, but I don't really understand how this can work. The inverse map is clearly not smooth at x=0. Do they mean that...

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 :)