Recent content by 4real4sure

Hello, I was going through the following paper: http://www.emis.de/journals/HOA/AAA/Volume2011/142128.pdf In page 6, immediately after equation (3.15), its written that "functions of the form v(t) are dense in L^2". I have been looking for proofs online which verifies the above statement but...

Hello, I was going through Perron method within the text and came across Lemma 1 which states that if u1,u2 are subharmonic on some domain D and satisfies Cauchy boundary conditions (for example), then so does max(u1,u2). I am quite confused in terms of proving the statement. How would one...

Hello, I've been wondering if there is any way to keep track of the divisibility tree. For instance, 5+5=10, and 1+4=5 and 2+3=5 hence 1+4+2+3=10. Now hypothetically, I know that '1' occurs at location 2, '4' occurs at location 1, '2' occurs at location 4 and '3' occurs at location 1 and they...

Hi everyone, I have a general question regarding KPM. Since kronecker product matrices have cartesian tiling, I was wondering if these could be made more efficient by implementing hexagonal sampling instead of cartesian within kronecker matrices. Is it possible to do that? I'm confused since...

I found out by applying laplace to each factor, s^2y(t)+4sy(t)+4y(t)=-7t(t+3) s^2y(t)+4sy(t)+4y(t)=-7t(t)-7y(3) y(t)(s^2+4s+11)=y(3) But from here, I am confused. Since in the question the value of u(t) was given to be e^-3t. Other wise I would have used laplace transform of u(t) which...

Homework Statement d'^2 (y)/dt + 4 (dy/dt) + 4y = -7(e^(-3t)). Here I need to forced response of this differential equation using laplace transform technique. Homework Equations The Attempt at a Solution I understand the part of converting each term to each laplace, d^2y/dt to...

Homework Statement A spherical droplet of radius R and effective mass density ρ. carries a total charge q in a gravity field g. What electric field E iz, will suspend the charged droplet? Millikan found by this method that all droplets carried integer multiples ofnegative charge e= -1.6 x...

I tried and I finally reached the solution. Thanks for all your support!

I tried to do it several times based on may understanding but for some reason I am so not able to reach to the solution. Any hint?

Homework Statement Charges Q, Q, and q lie on the corners of an equilateral triangle with sides of length a. Charge q lies on the top corner with Q and Q on the left and right corners. (a) What is the force on the charge q? (b) What must q be for E to be zero half-way up the altitudeat...

Here it is, A rigid body rotates with angular velocity 3 rad/sec which remains stable. r is the distance vector from origin to a point Q, the position of a particle in the body. The velocity u of the body at Q is given by u = w X r (where u, w ,r are vectors). The rigid body is rotating parallel...

It would be correct if you had units on there. I didn't get this

ax, ay, and az are unit vectors and I need to figure out the statement for the vector "w" which is in the attempt.

The last statement itself was an attempt and I need "confirmation" if it is okay or not. 3. The Attempt at a Solution w(vector)=w(1,-2,2) / 3 = (1,-2,2) I need confirmation if this is correct or not. In either case, reasoning would be much appreciated.

Homework Statement Rigid body is rotating with 3 radians per second about an axis parallel to ax - 2ay + 2az. Express this mathematically. Homework Equations ax - 2ay + 2az The Attempt at a Solution w(vector)=w(1,-2,2) / 3 = (1,-2,2) I need confirmation if this is correct or not...