Recent content by Grufey

Homework Statement Given a detector with 500 pixels, and a pixel size of 5 um, is it posible to register next signal? I = cos(2 π 4 x) were x is expressen in umHomework Equations fs = fs/2 The Attempt at a Solution My problem is with the pixel size, I mean, the sampling rate will be...

Homework Statement First, thanks in advace. Let us consider a microscope where the objective L1 has f1=20mm and magnification 10x. In the image plane is located a diafragm M with diameter 19mm (see fig). The size of the CCD is 4,8mm (vertical) x 5,6mm (horizontal). 20mm before of the CCD...

The set is convex due to every pair of points can be linked with a continuous line. Also is closed, because the condition greater or EQUAL. Accordingly with the definition, the complementary set is open. And finally the set is not bounded, it's wonder, there isn't any contidion about the maximum...

Hi, 939 I'll try to cast light on this question ;) First, let us consider a point in R² (X',Y'), such as X’ >0, Y’ > 0. Therefore, our graph will be in the first quadrant. Second, What does mean: X ≥ X' and Y ≥ Y’?. It represent an angle in the space. The vertex of the angle is the point...

I mean, the equations obtained, implies: \frac{\partial M}{\partial x}\frac{\partial \theta}{\partial y} = \frac{\partial M}{\partial y}\frac{\partial \theta}{\partial x} This relation is due to M is a function of a single variable, θ, and θ=θ(x,y). And the variable x, and y are relate via the...

Thanks Mark44 for casting more light on the problem. Now I'm completely sure of my calculus. My last question in this issue was if the reason is this, I quote: "the particle derivative in the variable x, is related with the partial derivative of the variabley. In other words, the surface...

Thanks for your reply. I have a few doubts. Accordingly with you, my calculus are right, perfect!. I'm not a complete foolish XD. In order to check the result. I consider a function: θ=xy^2, then \frac{dM}{d\theta} =\frac{\partial M}{\partial x}\frac{1}{y^2} = \frac{\partial M}{\partial...

Hi everyone! I'm not sure if this is the right forum to post my question. If I'm wrong, let me know it. The question: Let us consider the functions \theta=\theta(x,y), and M=M(\theta), where M is a operator, but i doesn't relevant to the problem. I need to know the derivative \frac{\partial...

Sorry I was too busy this week and I could not reply before. That's what I thought, it's only a notation. misleading notation. Regards

Hello I'm reading my old notes of QM, I found the definition of Pauli vector, as follow \vec{\sigma}=\sigma_1 e_x+\sigma_2e_y + \sigma_3 e_z Where e_x. e_y and e_z are unit vectors. So, here is my question. \sigma_i and e_i are elements of different nature. How can we define the product...

There are, too many optodesign softwares: Zemax, Code V, TRACERAY, Oslo. I recomend, Zemax. But, I must advice, it's not easy to learn anyone of them. Greetings

I don't know, but I thougt in the Lambert function If we define x^x=z, then, x=\frac{ln(z)}{W(ln(z)}, where W is the Lambert function. So we can write x^z=\left(\frac{ln(z)}{W(ln(z)}\right)^z, and then integrate. I know, that this is awfull, but, maybe it can help or give any clue.

try using, \cos 2x=\cos^2x-\sin^2x and \cos^2x/2=\sqrt{\frac{1+\cos x}{2}}

Hello. First, the definition: Let's a matrix, A, is called definite positive if, vAv^t>0 for all v (v vector). Here, I think you have the answer. http://mathworld.wolfram.com/PositiveDefiniteMatrix.html

Hello MikeyW. I'm not sure, but, sometimes in functional analisys, we say that, the function is continuous, except in sets of null measure. In this case, the function f(x,y)=1 if x>0, y>0, else f(x,y)=0, is continuous, except in sets of null measure.