Term Definition and 775 Threads

1. Write down the general term of each of the following sequences in simplest form: So far I have been using guess and check to find the solutions, but it doesn't seem much use when you get to a sequence more complicated like this: 1, -4, 7, -10, 13, ... I really need to find an equation that I...

It's part c I don't understand, why the expectation value equals to solid angle * sin3 i? I mean, what role does the solid angle play? Thank you

I've got a term paper due in a couple of weeks and I need to find a historical physicist to write it about. The paper will highlight his/her's contributions to physics and will be a bit on the technical side (including equations, maybe some derivations and proofs). I was wondering if anyone had...

I have a problem understanding the attached part of the book... Specifically how they derived this result for the Fs... For example I'll try to write: F_{1}^{\dagger}= - \frac{\partial W(Φ_{1},Φ_{2},Φ_{3})}{\partial Φ_{1}}|_{Φ_{1}=φ_{1}} If I do that for the O'Raifeartaigh superpotential I'll...

I am currently a freshman in a top 20 school. I am midway through my last term of the first year. I am depressed, far away from home, and my grades are falling(since the last term's finals). I am considering withdrawing for the term just to regain my peace of mind and life. I will probably be...

Homework Statement i got stucked here. below is the answer given. can anybody help please? Homework Equations The Attempt at a Solution

Is the term "loop" loosely defined in Faraday's law? A voltage will be induced in a loop of wire when the magnetic field flux through the loop changes If you're reading this, you probably know what happens when you hook up the leads from an oscilloscope to a microphone. Nothing, lol. There...

My mind has gone blank and I've suddenly forgotten basic algebra, please could someone give me direction on how to make P the subject of this equation? E = (P^2 C^2 + M^2 C^4)^1/2 + (P^2 C^2)^1/2 thanks for any help

Homework Statement {a_n} and {b_n} are two sequences given by a_n = (x)^{1/2^n}+(y)^{1/2^n} and b_n = (x)^{1/2^n}-(y)^{1/2^n}. Then find a_1 a_2 a_3 ... a_n in terms of x,y and b_n Homework Equations The Attempt at a Solution I tried substituting n=1,2,3 and so on for a few...

"Find the next term" After studying more math, I've been conflicted about this type of assignment commonly given to high schoolers. In the sequence 1, 4, 9, 16, ____ find the next term. On one hand, it's a good exercise and teaches pattern recognition. On the other though, it seems to go...

Reading over Alcubierre's paper on his "warp" drive (http://arxiv.org/abs/gr-qc/0009013), the metric in equation 3 has a velocity term, v, that doesn't seem to be needed anywhere. Even in the one spot where it seems potentially valuable, equation 12, he just call it =1 and essentially ignores...

Homework Statement I've done physics in a non-english medium and I want to know what is the technical term to call the incident where the image is flipped vertical through a mirror. I mean if we stand infront of a mirror and raise the right arm, the mirror image shows we're raising the left...

My first post, and a very long one... I have problems understanding the prolific use of a certain term in the rocket thrust equation and its validity. The general rocket thrust equation contains a term referred to as the pressure thrust. It is calculated as (p_e – p_a)Ae where p_e is the...

Imagine a straight line that contains both the center of the sun and the center of the earth. This line passes through a point on the surface of the Earth that is between those two points. As the Earth rotates, this point moves west, forming a kind of line on the surface of the earth. What...

Ok so i have the equation y'=y^2(y-3)(y-5)^3 I found the equilibrium positions to be y=0, y=3, y=5. For my phase diagram all the arrows are pointing up so the solutions are nodes? The last part asks Describe the long term behavior of the solution to the above differential equation with...

Hello to everyone, I urgently need to solve the following pde: ∂u/∂t +∂²u/∂x² = So*δ(x-xo)*sin(wo*t) It's the heat equation with a cyclic source. The lentgh of the cable is L. I have no clue how to do this with such a source, all i have learned was to do a separation of variables, but it...

I will be graduating with an engineering degree (mechanical) in May of 2014. The city that I currently live in is not where I want to stay after I graduate; however, my wife is well established in her career and it makes sense for us to stay here for a year or so in order to save up money etc...

Dear Forum, Does every sequence have a general term? What is the definition of the general term of a sequence? Best wishes

I'm trying to clarify for myself the relation between the stress-energy tensor and the mass scalar term in metric solutions to Einstein's equations. Maybe I should also say I'm trying to understand the energy tensor better, or how it relates to boundary conditions on the solutions. My...

First of all, I'm not sure if this thread belongs here or at the "Special & General Relativity" sub-forum, if I posted at the wrong place please move it. Homework Statement I encountered this problem working in my master's degree. I need to find the stress-energy tensor of the following...

Homework Statement combustion adds 1200kj/kg to the charge. what is the meaning of " charge" here. Homework Equations The Attempt at a Solution

Hi everyone, I'm reading Logic for mathematician form A.G. Hamilton, at some point the book explain what a free term is, but I'm not sure how to determine if t is free or not. I was wondering if one of you may have a link where I could read more about it. (I have find some info on wikipedia...

I have a question why is \frac{2x^2-1}{x^2+1} equal to 2-\frac{3}{x^2+1} ??

In the context of my work (linear differential equations), it can not be zero. But why?

Homework Statement Approximate the value of the integral of 6/(1+2x) with respect to x from 0 to 2. Use 4 subintervals of equal width and use the left endpoints. Homework Equations delta x = (b-a)/N The Attempt at a Solution The integral is the sum of 6/(1+i) from i = 0 to i = N-1 or 3...

Homework Statement Let ##\displaystyle a_n=\frac 1 2+\frac 1 3+...+\frac 1 n##. Then A)##a_n## is less than ##\displaystyle \int_2^n\frac{dx}{x}##. B)##a_n## is greater than ##\displaystyle \int_1^n\frac{dx}{x}##. C)##\displaystyle \lim_{n\rightarrow \infty} \frac{a_n}{\ln n}=1##...

I have to solve a bunch of exercises related to function series and in some of them they ask me whether a particular series converges uniformly if one differentiates it term by term. So here I came up with a doubt: When ##\sum_0^{\infty} f_n(x)## can be differentiated term by term? What...

Suppose we are given two projection operators H' and H'' such that H' + H'' = 1, i.e. that any vector can be written as V = V' + V'' = (H' + H'') V. In a formula for a projection of the Riemann tensor (see the thread "Projection of the Riemann tensor formula") I encountered the term...

We used to classify signals as 1D and 2D etc ie one dimensional and two dimensional. For example a periodic square wave signal is 1D and an image is a 2D signal etc (reference - Signals and systems by Simon Haykin and Barry Van Veen, 2nd edition , page 2). But the same periodic square wave...

In signal processing , what do the term 'feature' means? Feature extraction etc. For example, in audio signals what are the main features? -Devanand T

Origin of the term "chair" in academia? When I was very young, I wondered why professors (heads of departments) were said to have a "chair" in such-and-such subject. I thought of the story about King Louis XIV of France who was said to have a chair in (their equivalent of) the cabinet room...

Homework Statement I have two questions 1.Today,in my test paper,I got this sequence. Find the nth term formula 1,3,15,61,253 I didn't know how to start.This is clearly not an arithmetic or geometric sequence. Any help? 2. And is there any formula for finding the nth term of sequences...

Optimization - Why is there a constant term in the time equation?? Mod note: The OP apparently answered his own question. Homework Statement 1) A man can run at 8 km/hr and swim at 4 km/hr. He is currently 6 km from the shore of a lake, which is due east from him. He wants to get to a point...

Hi, I am trying understand if there is a quick way to figure out the impact of the X term in a quadratic equation. For example, by looking at the following equation, I know that it is a parabola (X^2) ; by looking at 24, I know that it is the y-intercept. However, I don't know what is the...

Google hasn't been very helpful on this one and my textbook once again assumes we are born with certain knowledge as it doesn't delve any further than, "Many practical engineering problems involve systems acted on by impulsive forcing terms" without further explanation. Isn't that nice... So...

Hello, This is not a homework, just trying to solve the previous exams and I'm stuck at one of them : Homework Statement Consider Fn(x)=1/(2*pi) * [ sin(n*x/2) / sin(x/2) ] Calculate: ∫ F2012(x) from -pi to pi Homework Equations The Attempt at a Solution I've tryed...

Solve the differential equation (5x+4y)dx+(4x-8y^3)dy=0 So M(x, y) = 5x+4y and N(x, y) = 4x-8y^3 Check \frac{\partial M}{\partial y} = 4 and \frac{ \partial N}{\partial x} = 4 check passed. f(x, y) = \int M \partial x + g(y) = \int 5x+4y \partial x + g(y) = \frac{5x^2}{2} + 4yx + g(y)...

Hello, could somebody please explain to me why in 4 of these solutions, the angular momentum final term about point p is mVfR + Icmω ? It is in huge attached solutions my teacher posted. Thank you very much in advance Here is the problem in case you are interested of Horne context. 4. A...

Can the term "distortion" be used interchangeably? Clipped sine wave = distortion Assume I run a 30hz tone through one of my dedicated mid-range loudspeakers. There's no doubt that the loudspeaker would bottom out. People often call this distortion. But the signal never clipped. It's the...

Hi, I'm trying to solve the flow profile inside an inhomogeneous porous material between two parallel moving plates (essentially Couette flow with a deviation), and I model my system by the following equations: \nabla^2 \mathbf{u} = p(x,y,z) \mathbf{u}\\ \nabla \cdot \mathbf{u} = 0...

term “scattering” more of a general process Is the term “scattering” more of a general process which incorporates the linear effects of reflection, refraction and diffraction?

Homework Statement I'm having a brain fart, how do you factor/simplify a fraction such as \frac{ab}{ab+cd} I keep thinking multiply by ab-bc but I'm not sure.

Is there a term to describe the phenomenon that observation seems to effect the outcome of superposition?

How exactly do you derive it without using tensors? You use Newton's frictional law on a 3d block of fluid, instead of just on fluid surfaces, but I can't 100% visualize how. So is there any simple derivation, or at least explanation? \mu \nabla ^2 \vec{V}

Like the topic,if in my system derivation, there is an independent gravitational force independent of the state variable, is my system linear? I believe it is not but my instructor is telling is it is. I'm thinking that if there is is an extra gravitational term,the output of the system does not...

The fibonacci sequence can be defined as $${F_n} = {F_{n - 1}} + {F_{n - 2}}$$ and specifying the initial conditions as $$\eqalign{ & {F_1} = 1 \cr & {F_2} = 1 \cr} $$  Also there exists a general formula for the fibonacci which is given by $${F_n} = {{{\varphi ^n} + {\psi ^n}} \over...

Solve the differential equation by separation of variables x \frac{dy}{dx} = 4y becomes \frac{1}{4y} dy = \frac{1}{x} dx Integrate to get \frac{1}{4} \ln{|y|} = \ln{|x|}+C I'm stuck here because I want to raise e to the power of both sides of the expression like e^{ \frac{1}{4} \ln{|y|}} =...

I've been thinking about chapter 11 of Griffiths' Introduction to Elementary Particles. In section 11.7, he gives the Lagrangian density \mathcal{L}=\frac{1}{2}(\partial_{\mu}\phi)(\partial^{\mu}\phi)+\frac{1}{2}\mu^{2}\phi^{2}-\frac{1}{4}\lambda^{2}\phi^{4} and shows that the minimum...

Here is the question: I have posted a link there to this topic so the OP can see my work.

I have two questions having to do with the Lorentz transformation for the time...some preamble first: The Lorentz transformation for time along the x-axis is t'=\frac{t-\frac{ux}{c^2}}{\sqrt{1-\frac{u^2}{c^2}}}, where u is the relative velocity of S'. Why is there a dependence on x...