Recent content by jamesb1

Wow, now that is quite interesting and it makes so much sense. Looks like I need to revise some combinatorics! Thank you again.

Thank you for your answer! I actually tried that approach before (of expanding using the Maclaurin series for ##(1-x)^{-1}##. I then couldn't continue after that as I never knew about this notion of the ##c_n## coefficient. Could you elaborate on how ##c_n## happens to be the cardinality of that...

Homework Statement I want to express the following expression in its Taylor expansion about x = 0: $$ F(x) = \frac{x^{15}}{(1-x)(1-x^2)(1-x^3)(1-x^4)(1-x^5)} $$ The Attempt at a Solution First I tried to rewrite the function in partial fractions (its been quite a while since I've last...

The other definitions in the paper I linked are not really necessary as this definition does not take any special insight from them. I gave the information needed specifically for I_n and M(I_n) because they're mentioned but other than that, it can pretty much be taken as a standalone definition...

I understand that, what I mean is I don't understand how it correlates with this definition; where the Lebesgue integral being zero implies that the measure μ is also 0.

I am reviewing this http://deeplearning.cs.cmu.edu/pdfs/Cybenko.pdf on the approximating power of neural networks and I came across a definition that I could not quite understand. The definition reads: where $I_n$ is the n-dimensional unit hypercube and $M(I_n)$ is the space of finite...

You're very right, thank you :)

I'm currently in my final year of BSc(Hons) in mathematics and computer science & A.I (applied math stream). Indeed, I'm starting to think about what masters I want to pursue and the kind of subject I would like to specialize in. I am really interested in quantum computation and the prospects of...

Hi I would like to know whether there will be LaTeX support added for the mobile app as well since the mobile app would be just 100% perfect if this feature would be added. I find it practically unusable without this support. Thank you

Why is it assumed that the method of separation of variables works when the boundary conditions of some boundary valued problem are homogeneous? What is the reasoning behind it?

Shouldn't the interval not contain variables though, to have a definite region? I know you can choose any x and fix it, but it seems indefinite to me. x should remain fixed instead of having x1 and x2, no? I am unsure how to attain values for both x and y such that the following inequality is...

As the title says, I need to find such a region. Taking any x, and any y1 and y2 I used the expression |F(x,y1) - F(x,y2)| and plugged in the function respectively for y1 and y2. Now I have to find values for x and y such that the following condition (Lipschitz condition) is satisfied: | 2x +...

But that means you CAN'T have linearly dependent and invertible linear transformations .. no?

Is the title statement true? Was doing some studying today and this caught my eye, haven't looked into linear algebra in quite a while so I'm not sure how it is true :/ Internet couldn't provide any decisive conclusions neither Many thanks

When it comes to converting Cartesian to polar coordinates, I sometimes still get mixed up on how to define the angle theta (if its -π <= theta <= π , or 0 <= theta <= 2π for example) depending on the position of the surface etc. Can anyone shed light on the definitive way on how to set this...