Example Definition and 845 Threads

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...

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?

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...

Homework Statement Using the comparison test determine if the infinite series for sin(3/n^2) converges or diverges. The Attempt at a Solution Well... these are pretty straight forward, and it's pretty obvious that this is convergent, but I'm having trouble applying the...

Hi guys is the example true? what will the clock 3 count when the light reach it

I'm trying to follow a very simple example example in a text (Marion/Thornton example 2.1) and I think my rusty calculus is tripping me up and I'm just being stupid. I understand how to derive the acceleration down the plane: \ddot{x}=g\sin\Theta but next they say 'we can find the...

"If AB+BC = 24 and AB = 10, THEN 10 + BC = 24 is an example of the ? Homework Statement "If AB+BC = 24 and AB = 10, THEN 10 + BC = 24 is an example of the ? Homework Equations A) Symmetric property of equality B) Substitution property of equality C) Addition property of equality D)...

Example of transitive but not well ordered set needed! My question pertains to the definition of ordinals. According to Thomas Jech's edition of set theory, a set is ordinal if it is both transitive and well ordered by membership. I've been poking around trying to find an example of a set which...

Hi All, Thermodynamics forbids perpetual motion based in its second law, but how should one deal with an isolated H atom, seen here as a machine? Is there a concrete perspective of its stopping? In its stationary and fundamental state may one observe dissipation? Thank you DaTario

I'm trying to visualize the relativity example given in the book. The one with 2 generals signing a treaty at ends of a train (the light in the middle goes on and they both sign when light reaches them). The observers claim that one of the generals signed first. However, the generals claim that...

This is not actually a homework question, just something I am wondering about. A specified charge density dependent on /theta is glued over the surface of a spherical shell and you are asked to find the potential inside and outside the sphere, which is done in the example using separation of...

Hi there. I've been reading Brian Greene's book "An Elegant Universe" for the sake of curiosity and one of his examples to demonstrate special relativity really confuses me about the entire concept. To start, this is my current understanding of SR, so please correct me if I am wrong: -The...

Homework Statement A toy train moves along the track at 9.0m/s. When the power is turned off, the train comes to a stop in 6.0s. The net force on friction acting on the train to stop it is Homework Equations F=ma The Attempt at a Solution how do i find mass and acceleration so...

I know that the canonical example of a covering set of S^1 is R with the exponential map e^(ix) and that visually, this can be pictured by curling R up in a spiral and letting the "shadow" of the points determine the map. However, I want to know if this is another example: The covering...

It seems to me that the eyes are an example of the photoelectric effect at work. If so, which is more effective; current technology, photosynthesis, or our eyes?

I read that the outer measure is not countably additive, but I can only think of cases where the outer measure is countably additive. Can anybody give me an example where the outer measure is not countably additive? Thanks

Hey I am looking for an example problems that have piezoelectrics generating electricity. I would like to have and use a simple problem in which a piezoelectric is squeezed to generate electricity. Does anyone know where I can find such problems and solutions?

Consider a case where 2 people are in a car driving in a straight line at sufficient speed. At some point the driver takes an abrupt 90 degree right turn and owing to reasons attributed to Newton’s first law the co-passenger swerves into the driver (i.e. to the left). My question is why...

Hello all, I have been trying to fill in the gaps in the example of a functional given in chapter 3 of Hartle's book "Gravity" and I am not having much luck. I exhausted wikipedia for help to no avail. Does anyone know of or can provide a good simple example of a functional or just the...

What could be a real-life example (so no imaginary units and stuff :approve:) where the product of two elimentary functions of one random variable has a meaningful interpretation. Let's say I have a function that maps my random monthy income to number of days I can live off it and another...

This isn't really a homework question, can someone just explain this bit from wikipedia? consider the space X which consists of the union of the two intervals [0,1] and [2,3]. The topology on X is inherited as the subspace topology from the ordinary topology on the real line R. In X, the set...

Hi, can anyone give me an example of a bounded operator on a Hilbert space that has dense range but is not surjective? (Preferably on a separable Hilbert space) Im pretty sure such an operator exists since the open mapping theorem requires surjectivity and not just dense range, but its just...

I would like an example in Latex of a product with indices n=1 to N for bN, all minus 1, finally equal to bZ. I have not been able to find the original Latex tutorials.

I am math teacher and was asked the classic question, "Where am I ever going to use this in life" I usually have a real word example, but for the cosecant function I am stuck (Besides higher level math classes.) Anyone know a specific example?

So since I've started learning up on SR, the way I look at some things is nothing like it used to be before. The other day I was sitting down looking about, when I went cross eyed for a moment. Then I realized something quite interesting. If you have an object in front of you and you cross...

Ok from other posts, everyone seems to say that it doesn't matter if you stick vectors into a matrix via columns or rows. So i want to prove this to myself using an example from my notes. The only problem is, I get different answers. Can someone correct me? from my notes it says "show (0...

Homework Statement How do you draw a bode plot? I have a simple equation: H(S)=s+10 but no school book. Can you help me understand?

I'm a bit confused here with determining the tension of a rope. A very simple example will do in this case. Let's consider a weight of G hanging from a weightless rope which is tied to a ring hanging from the ceiling. The weight pulls down on the rope with the force of G and the ring pulls up on...

Here is a link to the text, chapter 9... page 30: http://books.google.com/books?id=gQ8LAAAAYAAJ&printsec=frontcover&dq=einstein&ei=tondSZLWOpnGywTa_pHyDg#PPA30,M1 So I have been analyzing this thought experiment from a causal perspective and have found it to be quite unsatisfactory. The...

In some discussions here about quantum effects in the macro world, ZapperZ will only admit that things like superconductivity, Bose Einstein condensates etc. are good examples. But these are just macroscpic quantum coherent phenomena. Of course, if you have a flux qubit, you can directly...

Homework Statement Give an example of a ring R and a function f: R---->R such that f(a+b)=f(a)f(b) for all a,b in R. and f(a) is not the zero element for all a in R. Is your function a homomorphism? Homework Equations Let R and S be rings. A function f:R----->S is said to be a...

Homework Statement If G is an abelian group, show that H = { a in G | a^2=1} is a subgroup of G. Give an example where H is not a subgroup. The Attempt at a Solution For showing H is a subgroup of G, hh' in G and h^-1 in G. (a^2)(a^2) in G also a = a^-1 in G so H is a subgroup of G...

Hey all - this is my first post so I mght as well say hi - I'm not very smart, but find everyday physics interesting. I tried to look up Newton's Laws, but I can't figure out: Is a dirt bike or bicycle a good example of the f=ma principle? All the info I found states that the force is...