Form Definition and 1000 Threads

Hi, I know the weak form of the Poisson problem \nabla^2 \phi = -f looks like \int \nabla \phi \cdot \nabla v = \int f v for all suitable v. Is there a similarly well-known form for the slightly more complicated poisson problem? \nabla (\psi \nabla \phi ) = -f I am writing some finite...

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

How to solve this question. Please explain step by step.

Hi all Can someone please describe how the form factor used in Rutherford scattering is applicable to neutron probing of nuclei? Also, is the kinetic energy required to probe a given radius simply given by the de Broglie wavelength where momentum, p >= h-bar / Radius ? (Relativity...

Hey guys, I just want to ask on how do you determine the form of wave function for Schrodinger equation of finite potential well and potential barrier. Why is it ψ(x) = Ae^ikx + Be^-ikx (x < -a) ψ(x) = Fe^ikx (x > a) ψ(x) = Ce^μx + De^-μx (-a < x < a) for k^2 =...

C# Windows Form "Game": Movement All I wanted to do was to make a block move right/left across the window. I'm using VS 2010. No compiler errors and when I run it, it doesn't respond to any input. using System; using System.Windows.Forms; namespace Game { public partial class Form1...

Show that $ \displaystyle \text{Im} \ \exp \left( ae^{be^{i c \ x}} \right) = \exp \left( ae^{b\cos(cx)\cos (b\sin cx)} \right) \sin \left( a\sin (b\sin c x) e^{b\cos cx} \right) $.EDIT: Then by integrating $ \displaystyle f(z) = \frac{z \exp ( ae^{be^{ic \ x}} )}{z^{2}+d^{2}}$ around a...

Hi. I would like to ask a question about Chapter 15 in Srednicki's QFT book. In chapter 15, after eq. (15.12), he compares eq. (15.12) ## \mathrm{Im}\bm{\Delta}(k^2)=\frac{\mathrm{Im}\Pi (k^2)}{(k^2+m^2-\mathrm{Re}\Pi (k^2))^2 + (\mathrm{Im}\Pi (k^2))^2}## with eq. (15.8)...

I am currently working with Lie algebras and my research requires me to have matrix representations for any given Lie algebra and highest weight. I solved this problem with a program for cases where all weights in a representation have multiplicity 1 by finding how E_\alpha acts on each node of...

1. Linear or Circular Acceleration (Synchrotron) 2.I.e, which accelerator is safer in terms of radiation leakage and radiation outbreak. 3. I thought a Linac would be safer.

Can you make an educated guess on the amount of energy in the universe in the form of electromagnetic radiation (photons), considering the vast amount of photons moving in every direction throughout the vast universe, there is literally no point in the universe that you can be in and not observe...

Hello everyone, I'm working on a problem and it turns out that this equation crops up: 1 = cos^{2}(b)[1-(c-b)^{2}] where c > \pi Now I'm pretty sure you can't solve for b in closed form (at least I can't), so what I need to do is for some value of c, approximate the value of b to...

Any Kähler form (?) can be written in local coordinates as \omega = \frac{i}{2} \sum h_{ij} dz^i \wedge d z^j with h_{ij}(z) = \delta_{ij} + \mathcal O(z^2). But that would mean \bar \partial \omega = \frac{i}{2} \sum \frac{\partial h_{ij}}{\partial \bar z_k} d \bar z^k \wedge dz^i \wedge d...

Homework Statement I had to calculate an orbital speed for an arbitrary density ρ(r) I got: V = r*sqrt(G*ρ(r)*4π/3) Homework Equations I am supposed to leave this in integral form, which I don't know how to do as I do not understand calculus. ρ(r) is density of r, hence the...

So how do I convert r=4+4cos(theta) into rectangular form? I know that r^2 = x^2+y^2 and that rcos(theta) = x. Would the start of the solution be: sqrt(x^2 + y^2) = 4+4x If yes, I don't know where to go from there.

Using second mean value theorem in Bonnet's form show that there exists a $$p $$in $$[a,b]$$ such that $$\int_a^b e^{-x}cos x dx =sin ~p$$ I know the theorem but how to show this using that theorem .

In this note (http://sgovindarajan.wdfiles.com/local--files/serc2009/greenfunction.pdf) the Klein-Gordon retarded green function is derived on the form $$G_{ret}(x − x′) = \theta(t − t') \int \frac{d^3 \vec k}{(2\pi)^3 \omega_k} \sin \omega_k (t − t′) e^{i \vec{k}\cdot (\vec x - \vec x')}$$...

the actual problem is to show that the given matrix is similar to companion matrix here is the companion matrix Companion matrix - Wikipedia, the free encyclopedia ---------------- i know that if same frobenius canonical form then similar but i don't even know how to find the frobenius...

[solved] show all invariant subspaces are of the form i don't even know how to begin (Angry) C_x is a subspace spanned by x that belongs to V C_x = {x, L(x), L^2(x),...} edit: SOLVED

Homework Statement Let G:R2\rightarrowR be a C2 function such that G(tx,ty)=t2G(x, y). Show that: 2G(x,y)=(x,y).HG(0,0).(x,y)t The Attempt at a Solution G is C2, so its Taylor expansion is: G(x,y) = G(0,0) + \nablaG(0,0).(x,y) + \frac{1}{2}(x,y).HG(c).(x,y)t, where c lies on...

Homework Statement Hey guys, Here's the question. For a distinguishable set of particles, given that the single particle partition function is Z_{1}=f(T) and the N-particle partition function is related to the single particle partition function by Z_{N}=(Z_{1})^{N} find the following...

For a system I am studying the following sequence (which I would assume is quite common) came up: n1=1, n2=2, n3=4, n4=7, n5=11, n6=16, n7=22 ... i.e. the difference betweens two successive numbers grows with 1 as we move from (n_N-1, n_N) to (n_N,n_N+1). Is there a closed form expression f(k)...

Homework Statement In each part, the reduced echelon form of the augmented matrix of a system of linear equations is given. Find all solutions to the original system. a.  [1 0] [2] [0 1] [5]  b.  [1 0] [2] [0 0] [1]  c.  [1 0] [2] [0 0] [0]  d. ...

Hi, here is something I can't understand: When you fill a 100% tube with Mercury, close it in one end (the top) and stick it into a bowl of mercury, vacuum forms in the top of the tube. Where does the vacuum come from if it was not there to begin with? The tube was full of mercury to begin...

I have the ODE x''(t)+\frac{k}{m}x(t)=0. Given that the solution is of the form sin(ωt+ø), I plug this form into the original ODE and obtain ω=+\sqrt\frac{k}{m},-\sqrt\frac{k}{m}. And hence, I obtain two solutions of the ODE as follows: x_{1}(t)=Asin(\sqrt\frac{k}{m}t+ø)...

I have a finite sum of the form: ∑n=1Nexp(an+b√(n)) Is there any trick to evalute this sum to a closed form expression? e.g. like when a finite geometric series is evaluated in closed form.

Hi; I've been trying to solve the problem myself but i really don't what could be wrong; The problem says : Make the change of variables x=ucos−vsin y=usin+vcos where the angle 0<(phi)<2 is chosen in order to eliminate the cross product term in x^2+xy+y^2=6 Then find the standard form of...

Homework Statement A system obeys the equations: P=-(NU)/(NV-2AVU) and T=2CU1/2V1/2eAU/N/(N-2AU) Find the fundamental equation Hint: to integrate let s=Dunvme-Au Where D, n, m are constants to be determined. Homework Equations Aside from the given ones, V=Nv U=Nu...

Hello! :) The interpolating polynomial that interpolates at the following data: $f(5)=?,f(8)=14,f(12)=214$ is $4,125x^{2}-32,5x+10$. The corresponding interpolating polynomial in the Newton form is $p_{2}(x)=a_{0}+a_{1}(x-5)+a_{2}(x-5)(x-3)$.Which is the value of $a_{2}$? Is it 4,125 because...

I'm doing my homework but I'm lost on one thing. Let's say that we have a systems of equations like so: 2x1+3x2=y1 4x1+2x2=y2 Instead of setting it to a constant our teacher sets it to a variable, he says that to be able to compute this, the augmented matrix should look like: 2 3|1 0 4 1|0 1...

If dr = (dx, dy, dz) so, which is the correct form for d²r? Is (d²x, d²y, d²z) or (dy^dz, dz^dx, dx^dy) ?

Hi, I hope this question is appropriate for this forum - if not can anyone suggest a place to ask it? There is a lot of carbon based matter around, on an in the earth. But,as I understand it, other than gaseous forms all the other liquid and solid forms have been generated/created by living...

Find the slope of the tangent line to the curve f(x)=x-x^3 at the point (1,0) So, I went through and plugged (a+h) in everywhere I saw "x" (a+h)-(a+h)^3 Factoring: (a+h-a^3-3a^2h-3ah^2-h^3) I'm really stuck on what to do next...I don't see anything you can cancel/pull out? I know...

Homework Statement I need to obtain the minimum second order circuit of the function: Homework Equations The Attempt at a Solution I know that in order to get the minimum second order circuit, I need to use K-Map using both miniterms and maxiterm and compare them. My problem is to put the...

According to general relativity, if a remote observer monitors an object falling onto a black hole, (s)he will never see the moment when the object crosses the event horizon. Due to the time distortion, the falling object will hover over the event horizon forever. With that in mind, how...

So this is what I have tried so far playing around with exponent and radical properties to try and solve this textbook problem

Heeeeeeellllllllllllllooooooooooooo, I have a question about HTML and PHP: Firstly, I am using Apache2 and PHP5 (I think) and running it as a localhost. I created a simple HTML form that sends the variables via post to a PHP file; there are two variables with the names "nickname" and...

Hi everyone, :) Here's a question I encountered recently and did partway. I need your advice on how to proceed. Question: What can be said about the Jordan normal form of a linear transformation \(f:V\rightarrow V\) where \(V\) is a vector space over \(\mathbb{C}\), if we know that...

Hello, I'm here for another related intercept form problem of the formula: $$\displaystyle \frac{x}{a} + \frac{y}{b} \:=\:1$$ a) Find the equation of the line passing through (-5,-7) AND with y-intercept 3. b) Find the equation of the line passing with x-intercept 1/3 and y-intercept 2/5. I'm...

Greetings everyone, I need a help since the lecture of intercept form formula is $$X/A + Y/B = 1$$ are provied as limited examples and couldn't find exact information regarding for that. 6) Reduce the equation $$2x+3y = -1$$ to intercept form. 7) find the equation of the line whose slope is 3x...

Homework Statement r = 3sin\theta since x= rcos\theta x = 3sin\thetacos\theta and since: y = rsin\theta y = 3sin^2\theta Then I'm sort of stuck..

I managed to stumble upon a differential equation such as the one above while doing some torque calculations and am wondering if and how to find the solution to it. I'm not that well versed in differential equations, so any help would be appreciated. Edit: A method to graph an integral line for...

A recent post of chisigma rings me the bell of an old problem I thought of posting in a forum (either here or MMF). Is there any particular approach to computing a closed form for derivatives of certain smooth and continuous functions of $\mathbb{R}$? For example, it is easy to find the $n$-th...

Hi, All: Let X be a Reeb vector field, and let ω be a 1-form dual to X. Is ω necessarily a contact form? I know if we have a contact 1-form θ , and Zθ is the Reeb field associated with θ , then from the definition of Reeb field, we have θ (Zθ)=1, which mostly means that θ is...

Ok, so I have been searching around the internet for an answer to this and have not found anything besides the fact that electrons move in a quantum way, that is jumping from one place to another without passing through the space between those two places, which I am aware of. So the two main...

Hey! :o I am asked to convert the following grammar into Chomsky Form $$\Sigma=\{a,b,c,+\}, \Sigma_Q=\{S,V\},I=S$$ $$S -> S+S|V$$ $$V -> a|b|c$$ My idea is the following: $$S_0 \rightarrow S$$ $$S \rightarrow ST|V$$ $$T \rightarrow +S$$ $$V \rightarrow A|B|C$$ $$A \rightarrow a$$ $$B...

In the big crunch scenario, matter would clump together faster and faster, could a blob of this matter form a black hole, even if it had the necessary energy to maintain fusion or if it had no energy to burn up the matter? If the big crunch were to happen, and a single blob of mass existed at...

Hi, (not homework/academic) Is a closed form of the following expression possible? Either way, some pointers in the right direction would be really helpful. H(s)=\sum_{n=-\infty}^\infty \frac{k^n}{k^n+a/s} Thanks, D

I am trying to calculate the dual form of an SVM optimisation problem: Dual Form Optimsation Problem In my algorithm, I have a vector of alphas, vector of target outputs, and a Kernel matrix computing upfront. However, I am stuck as to what indices alpha and j should be taking here...

Hi I'm taking abstract linear algebra course and having trouble visualising bilinear form and inner products. I can visualise vector spaces, span, dimensions etc but haven't managed to figure out how to visualise this yet. Could someone please explain it to me in a visual way? I can't understand...