Recent content by caduceus

I have a non-linear differential equation and I wonder whether it has a soliton solution or not. How can I approach to the problem? So far I have never dealt with non-linear differential equations, hence, any suggestion is appreciated.

Actually it should work for and point in Ac except 0, for instance, for simplicity, we can take r=|a|/2 and we can take |a| instead of 1, then, B(|a|,|a|/2)={x \in Ac : |x|+|a|< |a|/2 for x \neq |a| and 0< |a|/2 for x=|a|}={|a|} since again |x|+|a|< |a|/2 is not correct.

So you mean, since we cannot approximate zero by only the elements of Ac for any r>0; B(0,r)={x \in Ac : |x|< r for x \neq 0 and 0< r for x=0}=(-r,r) Then for the interval (-r,r) around 0, there exist many elements from A. Even though we can take r as small as we want, there exists...

Homework Statement (R,dPO) - i.e. with post-office metric A=(0,1) My question is how to find ext(A) Homework Equations ext(A)=int(Ac) dPO(x,y)= |x|+|y| for x\neqy and 0 for x=y The Attempt at a Solution As from the definition of an interior point, st. For every a\inA and \epsilon>0...

No! Ohm's law is still valid. Only when the time is shorter than \tau (which we will figure out when we solve the DE) Ohm's law turns out an invalid assumption. Because after time \tau, electrostatic equilibrium is reached, and finding \tau is our concern.

\vec \nabla \cdot \vec J = -\frac{\partial\rho}{\partial t} and you should use the relation: \vec J = \sigma\vec E where \vec\nabla \cdot \vec E=\frac{\rho}{\epsilon}

You can use the basic Bessel relation, i.e; let k\rho=x e^{(x/2)(t-1/t)}=\sum J_n(x) t^n then make the transformation t=e^{i\alpha} st. \alpha=\theta+\pi/2 and then substitute them all in the Bessel relation, then you can obtain the given result.

I appologize for my ignorance. I am a new learner as well, and just trying to figure out the meaning of quantum mechanics rather than just doing some algebra. However, what if a wave function is just a real constant? Will not we get a zero fluctuation in momentum?

Oh, I guess I can see the point now. You mean square integrability. That is why I should use Delta function. Thank you.

I couldn't understand that why the Fourier integral is meaningless for f(x)=A*cos(ax) ? Any comments will be appreciated.

I guess if we proceed it, we will get back into the starting integral and can obtain no solution.

Homework Statement Is there any way to evaluate such an integral; \int e^{2x}x^{-1}dx Any attempts will be appreciated.

Thanks for your assistance.

Homework Statement There is a heavy box across the floor, and you apply a horizontal force just sufficient to get the box moving. As the box starts moving, you continue to apply the same force. Show that the acceleration of the box, once it gets started, is a=(us-uk)*g Homework...

Oh, I got the point! Thanks for replying..